The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions
Abstract
In this paper, we primarily study the Pogorelov-type C2 estimates for (k-1)-convex solutions of the sum Hessian equation under the assumption of semi-convexity, and apply these estimates to obtain a rigidity theorem for global solutions satisfying the corresponding conditions. Furthermore, we investigate the Pogorelov estimates and rigidity theorems for solutions to the parabolic versions under similar conditions. These results extend the works of He-Sheng-Xiang-Zhang-2022-CCM and Liu-Ren-2023-JFA.
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