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arXiv · 2610.06529

On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds

Rémi Delloque
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Abstract

We study a general class of fully non-linear elliptic Hessian equations on compact Riemannian manifolds. In particular, we replace the standard assumption that the equation is a symmetric function of the eigenvalues of the Hessian made by Caffarelli, Nirenberg and Spruck by a weaker one. After deriving a priori estimates for solutions under suitable assumptions on the equation, we solve it with a continuity method.

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Rémi Delloque. 2026-10-05. On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds. https://arxiv.org/abs/2610.06529

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