On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$

Siyuan Lu; Marcin Sroka

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arXiv · 2602.14946

On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$

Siyuan Lu·Marcin Sroka

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Abstract

We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation $\sigma_2/\sigma_1=1$ in $\mathbb{R}^n$. The proof is based on the observation that after rewriting the quotient operator as the $\sigma_2$ operator, acting on a new function, one can refer to the recent result of Shankar and Yuan on Liouville's theorem for $\sigma_2$ equation.

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Siyuan Lu, Marcin Sroka. 2026-02-16. On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$. https://arxiv.org/abs/2602.14946

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