论文标题
pogorelov type $ c^2 $ sum hessian方程和刚性定理的估计值
Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity theorem
论文作者
论文摘要
我们主要研究pogorelov $ c^2 $估计的解决方案解决方案的解决方案。我们在某些条件下分别建立了$ k $ convex解决方案和可允许的解决方案的Pogorelov型$ C^2 $估计。此外，我们采用此类估计来获得欧几里得空间中$ k $ -convex解决方案的刚性定理。
We mainly study Pogorelov type $C^2$ estimates for solutions to the Dirichlet problem of Sum Hessian equations. We establish respectively Pogorelov type $C^2$ estimates for $k$-convex solutions and admissible solutions under some conditions. Furthermore, we apply such estimates to obtain a rigidity theorem for $k$-convex solutions of Sum Hessian equations in Euclidean space.
