The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions

Weizhao Liang; Jin Yan; Hua Zhu

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arXiv · 2412.11822

The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions

Weizhao Liang·Jin Yan·Hua Zhu

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Abstract

In this paper, we primarily study the Pogorelov-type $C^2$ 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 \cite{He-Sheng-Xiang-Zhang-2022-CCM} and \cite{Liu-Ren-2023-JFA}.

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Weizhao Liang, Jin Yan, Hua Zhu. 2024-12-16. The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions. https://arxiv.org/abs/2412.11822

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