The degenerate J-flow and the Mabuchi energy on minimal surfaces of general type

TL;DR

This paper studies the degenerate J-flow on Kahler surfaces, proving key properties and linking it to the Mabuchi energy's properness on minimal surfaces of general type, advancing understanding of complex geometric flows.

Contribution

It establishes existence, uniqueness, and convergence of the degenerate J-flow on Kahler surfaces and connects these results to the properness of the Mabuchi energy on certain Kahler classes.

Findings

Proved existence and convergence of the degenerate J-flow.

Established properness of the Mabuchi energy on specific Kahler classes.

Linked geometric flow behavior to energy functional properties.

Abstract

We prove existence, uniqueness and convergence of solutions of the degenerate J-flow on Kahler surfaces. As an application, we establish the properness of the Mabuchi energy for Kahler classes in a certain subcone of the Kahler cone on minimal surfaces of general type.