Interior Hessian estimates for $k$-convex solutions of Hessian quotient equations

Zhisu Li; Ke Wu

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arXiv · 2610.18252

Interior Hessian estimates for $k$-convex solutions of Hessian quotient equations

Zhisu Li·Ke Wu

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Abstract

We study interior Hessian estimates for $k$-convex solutions of Hessian quotient equations $\frac{σ_k(D^2u)}{σ_\ell(D^2u)}=1$ with $2\leq k\leq n$, $0 \leq \ell < k$, and $k-\ell \in\{1,2\}$. We first adopt the unified quantitative separation-propagation method of Li--Wu [LW26b] to derive a doubling inequality, and then use the compactness argument of Shankar--Yuan [SY25] to obtain the estimates. This approach also applies to a class of general Hessian equations.

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BibTeX RIS

Zhisu Li, Ke Wu. 2026-10-13. Interior Hessian estimates for $k$-convex solutions of Hessian quotient equations. https://arxiv.org/abs/2610.18252

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