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arXiv · 2606.27003

Pogorelov type interior $C^2$ estimate for sum Hessian quotient equations on Riemannian manifolds

Guanghan Li Chenyang Liu
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Abstract

In this paper, we mainly study the interior $C^{2}$ estimates for a class of sum Hessian quotient equations on Riemannian manifolds. For $0\leq l<k< n$, we establish interior $C^{2}$ estimates at the center of a geodesic ball. Let $\Omega$ be a bounded domain (with smooth boundary) on Riemannian manifold. For $0\leq l<k\leq n$, we establish Pogorelov type estimates on $\Omega$ with the vanishing Dirichlet boundary condition.

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Guanghan Li Chenyang Liu. 2026-06-25. Pogorelov type interior $C^2$ estimate for sum Hessian quotient equations on Riemannian manifolds. https://arxiv.org/abs/2606.27003

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