We study the conformal deformation for prescribing scalar curvature function on Cartan-Hadamard manifold M^n(n≥3) with strongly negative curvature. By employing the super- subsolution method and a careful constructi...We study the conformal deformation for prescribing scalar curvature function on Cartan-Hadamard manifold M^n(n≥3) with strongly negative curvature. By employing the super- subsolution method and a careful construction for the supersolution, we obtain the best possible asymptotic behavior for near infinity so that the problem of complete conformal deformation is solvable. In more general cases, we prove an asymptotic estimation on the solutions of the conformal scalar curvature equation.展开更多
The author considers the problem of deforming the metric on a complete negatively curved surface conformal to another metric whose Gauss curvature is nonpositive.
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie con...The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α~k-derivations of multiplicative Hom-Lie conformal algebras and study their properties.展开更多
基金Project partially supported by the NNSF of China
文摘We study the conformal deformation for prescribing scalar curvature function on Cartan-Hadamard manifold M^n(n≥3) with strongly negative curvature. By employing the super- subsolution method and a careful construction for the supersolution, we obtain the best possible asymptotic behavior for near infinity so that the problem of complete conformal deformation is solvable. In more general cases, we prove an asymptotic estimation on the solutions of the conformal scalar curvature equation.
文摘The author considers the problem of deforming the metric on a complete negatively curved surface conformal to another metric whose Gauss curvature is nonpositive.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171055, 11471090 and 11301109)Natural Science Foundation of Jilin Province (Grant No. 20170101048JC)
文摘The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α~k-derivations of multiplicative Hom-Lie conformal algebras and study their properties.
