Interior Regularity for a generalized Abreu Equation

TL;DR

This paper investigates the interior regularity of solutions to a generalized Abreu Equation within n-dimensional polytopes, establishing interior estimates based on the assumption of uniform K-stability.

Contribution

It provides new interior regularity results for the generalized Abreu Equation under uniform K-stability assumptions.

Findings

Established interior estimates for solutions.

Connected K-stability with solution regularity.

Extended regularity theory to generalized Abreu Equations.

Abstract

We study a generalized Abreu Equation in $n$-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform $K$-stability.