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arXiv · 2609.24549

Interior estimates for Hessian quotient equations

Guohuan Qiu·Jin Yan
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Abstract

We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator differ in degree by one or two. Counterexamples show that this degree range is optimal. The proof combines a new nonlinear comparison function, a doubling maximum principle, and a Pogorelov estimate.

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Guohuan Qiu, Jin Yan. 2026-09-21. Interior estimates for Hessian quotient equations. https://arxiv.org/abs/2609.24549

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