In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece...In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.展开更多
Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f...Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds.展开更多
Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard to...Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.展开更多
The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is comp...The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.展开更多
We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radic...We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.展开更多
In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, m...In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.展开更多
In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.
The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Ki...In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.展开更多
In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigrou...In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space <em>E</em><sub>0</sub> to <em>E<sub>k</sub></em>, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.展开更多
Scattering theory plays the main role in the study of manifolds and the Laplacian spectrum. In this article, we process justifying the continuous Laplacian spectrum <img src="Edit_f17ab17a-8b55-4464-bd44-...Scattering theory plays the main role in the study of manifolds and the Laplacian spectrum. In this article, we process justifying the continuous Laplacian spectrum <img src="Edit_f17ab17a-8b55-4464-bd44-93ef0c3c0e35.png" width="30" height="24" alt="" /> and <img src="Edit_1da8a7e5-88fe-4053-96c6-052df6009009.png" width="30" height="25" alt="" /> on a complete Riemannian manifold. (<em>M</em>,<em>g<sub>i</sub></em>) is categorized by the use of bounded curvature of the metric. In particular, the covariant derivative is limitedly considered as an application in the geodesic distance from a fixed point.展开更多
In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup ...In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.展开更多
In this paper,we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds.Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a...In this paper,we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds.Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a class of complete Hermitian manifolds.展开更多
First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds w...First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.展开更多
In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we...In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive(resp.non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive(resp.negative)real bisectional curvature.These theorems generalize the results[5,6]proved recently by L.Ni on Kähler manifolds to Hermitian manifolds.We also derive an integral inequality for a holomorphic map between Hermitian manifolds.展开更多
This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generaliz...This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li's results in [2] and [3].展开更多
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.
基金supported partly by the NationalNatural Science Foundation of China(12071437)the Natural Science Foundation from the Education Department of Anhui Province(KJ2020A0044)+2 种基金the Research Fund Project of Chaohu University(KYQD-2023016)the High Level Scientific Research Achievement Award Cultivation Project of Chaohu University(kj20zkjp04)the Key Construction Discipline of Chaohu University(kj22zdjsxk01)。
文摘Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds.
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.
文摘The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.
文摘We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.
文摘In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.
文摘In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.
文摘The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
基金Supported by the NNSF of China(10231010)the Trans-Century Training Programme Foundation for Talents by the Ministry of Education of China+1 种基金the Natural Science Foundation of Zhejiang Province(101037) Fudan Postgraduate Students Innovation Project(CQH5928002)
文摘This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
文摘In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.
文摘In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space <em>E</em><sub>0</sub> to <em>E<sub>k</sub></em>, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.
文摘Scattering theory plays the main role in the study of manifolds and the Laplacian spectrum. In this article, we process justifying the continuous Laplacian spectrum <img src="Edit_f17ab17a-8b55-4464-bd44-93ef0c3c0e35.png" width="30" height="24" alt="" /> and <img src="Edit_1da8a7e5-88fe-4053-96c6-052df6009009.png" width="30" height="25" alt="" /> on a complete Riemannian manifold. (<em>M</em>,<em>g<sub>i</sub></em>) is categorized by the use of bounded curvature of the metric. In particular, the covariant derivative is limitedly considered as an application in the geodesic distance from a fixed point.
文摘In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.
基金supported in part by NSFC(11625106,11571332,11721101)the second author was supported by the Fundamental Research Funds for the Central Universities(19lgpy239)。
文摘In this paper,we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds.Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a class of complete Hermitian manifolds.
基金Project supported in part by the National Natural Science Foundation of China (10771174,10601040,10971170)Scientific Research Foundation of Xiamen University of Technology (700298)
文摘First of all, using the relations (2.3), (2.4), and (2.5), we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.
基金supported by National Natural Science Foundation of China(12001490)Natural Science Foundation of Zhejiang Province(LQ20A010005).
文摘In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive(resp.non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive(resp.negative)real bisectional curvature.These theorems generalize the results[5,6]proved recently by L.Ni on Kähler manifolds to Hermitian manifolds.We also derive an integral inequality for a holomorphic map between Hermitian manifolds.
基金Supported partially by the NNSF of China(10871171)
文摘This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li's results in [2] and [3].