Energy functionals and K\"ahler-Ricci solitons
Haozhao Li
TL;DR
This paper extends energy functionals to K"ahler-Ricci solitons, establishing their properness as equivalent to the existence of such solitons and exploring their boundedness and relation to invariants.
Contribution
It generalizes Chen-Tian energy functionals to K"ahler-Ricci solitons and links their properness to the existence of these solitons.
Findings
Properness of energy functionals is equivalent to existence of K"ahler-Ricci solitons
Lower boundedness of functionals relates to holomorphic invariants
Discusses the relation between energy functionals and Tian-Zhu invariant
Abstract
In this paper, we generalize Chen-Tian energy functionals to K\"ahler-Ricci solitons and prove that the properness of these functionals is equivalent to the existence of K\"ahler-Ricci solitons. We also discuss the equivalence of the lower boundedness of these functionals and their relation with Tian-Zhu's holomorphic invariant.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research