Extremal K\"ahler metrics

By G'abor Sz'ekelyhidi. 2014

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This paper is a survey of some recent progress on the study of Calabi's extremal K\"ahler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then turn to the question of what one expects when no extremal metric exists.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1d38fbf02eb3ad612d1b1fe9231de1b2a61b4434