By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exist...By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈M = T1.0M／o（M）, and then the horizontal Laplace operator NH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained展开更多
In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles ...In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.展开更多
Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities.We introduce a series of new invariant plurigeneraδm,m∈Z+for a strongly pseudoconvex CR manifold.The main purpo...Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities.We introduce a series of new invariant plurigeneraδm,m∈Z+for a strongly pseudoconvex CR manifold.The main purpose of this paper is to present the following result:Let X1and X2be two compact strongly pseudoconvex embeddable CR manifolds of dimension 2n-1 3.If there is a non-constant CR morphism from X1to X2,thenδm(X2)δm(X1)whereδm(Xi)is the plurigeneus of Xi(see Definition 2.4).展开更多
This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solution...This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.展开更多
In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of th...In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the process.We prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.展开更多
A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if ...A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.展开更多
We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R...We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.展开更多
The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equat...The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.展开更多
Let （M<sup>n</sup>, T） be a smooth involution on a smooth closed n-dimensional manifold M<sup>n</sup>. Let F<sup>n-k</sup> be the union of those （n-k）-dimensional components of ...Let （M<sup>n</sup>, T） be a smooth involution on a smooth closed n-dimensional manifold M<sup>n</sup>. Let F<sup>n-k</sup> be the union of those （n-k）-dimensional components of the fixed point set F of T and let v<sup>k</sup> denote the normal bundle of F<sup>n-k</sup> in M<sup>n</sup>. Czes Kosniowski and R. E. Strong have展开更多
In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued.
基金Supported by the National Natural Science Foundation of China (10571144,10771174)Program for New Centery Excellent Talents in Xiamen University
文摘By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈M = T1.0M／o（M）, and then the horizontal Laplace operator NH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained
基金the National Natural Science Foundation of China(11688101 and 11431013)the National Natural Science Foundation of China(12022110,11201347 and 11671306).
文摘In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.
基金supported by the Start-Up Fund from Tsinghua University and National Natural Science Foundation of China(Grant No.11401335)
文摘Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities.We introduce a series of new invariant plurigeneraδm,m∈Z+for a strongly pseudoconvex CR manifold.The main purpose of this paper is to present the following result:Let X1and X2be two compact strongly pseudoconvex embeddable CR manifolds of dimension 2n-1 3.If there is a non-constant CR morphism from X1to X2,thenδm(X2)δm(X1)whereδm(Xi)is the plurigeneus of Xi(see Definition 2.4).
基金supported by the Hunan Provincial Innovation Foundation for Postgraduate(CX2013A003)the NNSF(11171351,11361078)SRFDP(20120162110021)of China
文摘This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
文摘In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is considered.In this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the process.We prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.
基金supported by National Natural Science Foundation of China (Grant Nos.12131012, 12001007 and 11821101)Beijing Natural Science Foundation (Grant No. 1222003)Natural Science Foundation of Anhui Province (Grant No. 1908085QA03)。
文摘A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.
基金supported by the National Science Centre of Poland (Grant No. 2013/09/B/ST1/01963)
文摘We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.
基金supported by the projects of the DGISPI(Spain)(Ref.MTM2011-26119,MTM2014-57113)the UCM Research Group MOMAT(Ref.910480)
文摘The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.
基金Supported by the National Natural Science Foundation of China
文摘Let （M<sup>n</sup>, T） be a smooth involution on a smooth closed n-dimensional manifold M<sup>n</sup>. Let F<sup>n-k</sup> be the union of those （n-k）-dimensional components of the fixed point set F of T and let v<sup>k</sup> denote the normal bundle of F<sup>n-k</sup> in M<sup>n</sup>. Czes Kosniowski and R. E. Strong have
文摘In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued.
