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arXiv · 2405.03074

Sup-slopes and sub-solutions for fully nonlinear elliptic equations

Bin Guo·Jian Song
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Abstract

We establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on closed Riemannian or hermitian manifolds, including both hessian and hessian quotient equations. It settles an open problem of Li and Urbas. Such a condition is based on an analytic slope invariant analogous to the slope stability and the Nakai-Moishezon criterion in complex geometry. As an application, we solve the non-constant $J$-equation on both hermitian manifolds and singular K\"ahler spaces.

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Bin Guo, Jian Song. 2024-05-05. Sup-slopes and sub-solutions for fully nonlinear elliptic equations. https://arxiv.org/abs/2405.03074

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