Global viscosity solutions of generalized Kahler-Ricci flow

TL;DR

This paper proves the existence and uniqueness of global weak solutions to the generalized Kahler-Ricci flow on smooth manifolds using viscosity theory, highlighting potential extensions and correcting prior literature errors.

Contribution

It introduces a viscosity approach to establish global solutions for the generalized Kahler-Ricci flow on smooth manifolds, addressing gaps in existing research.

Findings

Existence of unique global weak solutions established

Viscosity methods successfully applied to complex geometric flows

Discussion on extending results to singular settings

Abstract

We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth background data. We discuss the possibility of extending these results to more singular settings, pointing out a key error in the existing literature on viscosity solutions to complex Monge-Ampere equations/Kahler-Ricci flow.