Lower bound of modified $K$-energy on a Fano manifold with degeneration for K\"ahler-Ricci solitons

TL;DR

This paper extends Tosatti's method to analyze the lower boundedness of modified K-energy on Fano manifolds and explores its implications for the stability of K"ahler Ricci solitons' deformation space.

Contribution

It introduces a new approach to study the lower bounds of modified K-energy and applies it to the relative K-stability of K"ahler Ricci solitons.

Findings

Extended Tosatti's method to Fano manifolds

Established lower bounds for modified K-energy

Analyzed stability of K"ahler Ricci solitons' deformation space

Abstract

In this paper, we extend Tosatti's method to study the lower boundedness of modified $K$-energy on a Fano manifold and apply this result to study the relative $K$-stability of the deformation space of a K\"ahler Ricci soliton.