In this paper,we study the multiplicity of the set of k-admissible radial solutions of a k-Hessian system with a nonlinear operator and gradients.Based on appropriate assumptions about f_(i)(i=1,2),several findings co...In this paper,we study the multiplicity of the set of k-admissible radial solutions of a k-Hessian system with a nonlinear operator and gradients.Based on appropriate assumptions about f_(i)(i=1,2),several findings concerning the multiplicity of k-admissible radial solutions are established via fixed point index theorem.展开更多
The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundl...The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12461039)the Natural Science Foundation of Qinghai Province(Grant No.2024-ZJ-931)。
文摘In this paper,we study the multiplicity of the set of k-admissible radial solutions of a k-Hessian system with a nonlinear operator and gradients.Based on appropriate assumptions about f_(i)(i=1,2),several findings concerning the multiplicity of k-admissible radial solutions are established via fixed point index theorem.
文摘The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.
