Relative K-stability for Kähler manifolds

Relative K-stability for Kähler Manifolds

We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of relative K-stability for Kähler manifolds, we prove that Kähler manifolds admitting extremal Kähler metrics are relatively K-stable. Along the way, we prove a general Lp lower bound on the Calabi functional involving test configurations and their associated numerical invariants, answering a ques...

Relative K-stability and Modified K-energy on Toric Manifolds

Abstract. In this paper, we discuss the relative K-stability and the modified K-energy associated to the Calabi’s extremal metric on toric manifolds. We give a sufficient condition in the sense of convex polytopes associated to toric manifolds for both the relative Kstability and the properness of modified K-energy. In particular, our results hold for toric Fano manifolds with vanishing Futaki-...

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

One Introduction to Kähler Manifolds