Remarks on modified Ding functional for toric Fano manifolds

TL;DR

This paper characterizes relative Ding stability for toric Fano manifolds through the behavior of the modified Ding functional, introducing the concept of pseudo-boundedness from below, and discusses similar properties for general Fano manifolds.

Contribution

It introduces the notion of pseudo-boundedness from below for the modified Ding functional and characterizes relative Ding stability for toric Fano manifolds.

Findings

Characterization of relative Ding stability via the modified Ding functional

Introduction of pseudo-boundedness from below concept

Discussion on pseudo-boundedness of Ding/Mabuchi functionals for general Fano manifolds

Abstract

We give a characterization of relative Ding stable toric Fano manifolds in terms of the behavior of the modified Ding functional. We call the corresponding behavior of the modified Ding functional the pseudo-boundedness from below. We also discuss the pseudo-boundedness of the Ding / Mabuchi functional of general Fano manifolds.