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arXiv · 2610.03062

A Comparison Pogorelov Estimate for Graphical $σ_k$-Curvature Equations

Jundong Zhou
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Abstract

We establish comparison Pogorelov estimates for admissible solutions of graphical $σ_k$-curvature equations, extending the two-surface estimate of Qiu and Yan for the graphical scalar curvature equation. The comparison graph is assumed only to be $k$-admissible, with a bounded slope and a positive interior gap that vanishes on the boundary. The estimates cover $2\le k<n$ for prescribed data $f(x,u)$, and $n/2\le k<n$ for general data $f(x,u,Du)$. The proof combines the two-surface localization and mixed Gårding comparison of Qiu and Yan with Yan's spectral concavity inequality and an angle-function weight.

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Jundong Zhou. 2026-10-02. A Comparison Pogorelov Estimate for Graphical $σ_k$-Curvature Equations. https://arxiv.org/abs/2610.03062

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