Fully non-linear parabolic equations on compact manifolds with a flat hyperk\"ahler metric

TL;DR

This paper extends previous work on fully non-linear elliptic equations on compact hyperk"ahler manifolds to the parabolic case, aiming to address problems in hyperhermitian geometry.

Contribution

It introduces a parabolic framework for non-linear equations on hyperk"ahler manifolds, expanding the analytical tools available in hyperhermitian geometry.

Findings

Extension of elliptic to parabolic equations on hyperk"ahler manifolds

Potential applications to hyperhermitian geometry problems

Development of new analytical methods for non-linear PDEs

Abstract

Our recent work about fully non-linear elliptic equations on compact manifolds with a flat hyperk\"ahler metric is hereby extended to the parabolic setting. This approach will help us to study some problems arising from hyperhermitian geometry.