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

2024/05/05 by Bin Guo, Jian Song, Guo, Bin +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2405.03074

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 Kähler spaces.

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