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arXiv · 2604.23349

Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions

Xinqun Mei·Jin Yan
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Abstract

In this paper, we study the interior $C^{2}$ estimates for Hessian quotient equations $\frac{\sigma_{3}(D^{2}u)}{\sigma_{l}(D^{2}u)}=1$ for $l=1, 2$, in arbitrary dimensions, under the natural ellipticity and semi-convexity conditions. We further derive analogous results for the corresponding sum Hessian equations. In addition, we establish several rigidity results.

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Xinqun Mei, Jin Yan. 2026-04-25. Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions. https://arxiv.org/abs/2604.23349

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