On the lower bound of the K energy and F functional

TL;DR

This paper establishes a fundamental equivalence between the boundedness of the K energy and the F functional in the context of Kahler geometry, leveraging Perelman's results on Kahler Ricci flow.

Contribution

It proves that the K energy is bounded below if and only if the F functional is bounded below in the canonical Kahler class, connecting two important functionals.

Findings

K energy bounded below iff F functional bounded below

Utilizes Perelman's results on Kahler Ricci flow

Provides a criterion for stability in Kahler geometry

Abstract

Using Perelman's results on Kahler Ricci flow, we prove that the K energy is bounded from below if and only if the F functional is bounded from below in the canonical Kahler class.