Hessian estimates for the sigma-2 equation in dimension four

Ravi Shankar; Yu Yuan

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arXiv · 2305.12587

Hessian estimates for the sigma-2 equation in dimension four

Ravi Shankar·Yu Yuan

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Abstract

We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher $n\ge 5$ dimensions.

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Ravi Shankar, Yu Yuan. 2023-05-21. Hessian estimates for the sigma-2 equation in dimension four. https://arxiv.org/abs/2305.12587

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