Fully non-linear parabolic equations on compact Hermitian manifolds

TL;DR

This paper introduces a new concept of parabolic C-subsolutions for fully non-linear parabolic equations on compact Hermitian manifolds, unifying the analysis of various geometric flows.

Contribution

It extends the theory of C-subsolutions to parabolic equations, providing a unified framework for studying geometric flows on Hermitian manifolds.

Findings

Developed the notion of parabolic C-subsolutions.

Unified approach for analyzing geometric flows.

Extended elliptic C-subsolution theory to parabolic setting.

Abstract

A notion of parabolic C-subsolutions is introduced for parabolic equations, extending the theory of C-subsolutions recently developed by B. Guan and more specifically G. Sz\'ekelyhidi for elliptic equations. The resulting parabolic theory provides a convenient unified approach for the study of many geometric flows.