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Mathematics > Analysis of PDEs
Title: Sup-slopes and sub-solutions for fully nonlinear elliptic equations
(Submitted on 5 May 2024)
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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