Almost convexity of the Mabuchi functional in singular settings
Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis August 21, 2024 - August 23, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
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Almost convexity of the Mabuchi functional in singular settings
The Mabuchi functional M was introduced by Mabuchi in the 80's in relation to the existence of canonical metrics on a compact Kähler manifold. The critical points of M are indeed constant scalar curvature Kähler (cscK) metrics. Recently, Chen and Cheng proved that the existence of a (smooth) cscK metric is equivalent to the properness of such functional. In order to look for singular metrics, it is then natural to study the properties of the Mabuchi functional in singular settings. In this talk we prove that this functional is (almost) convex in the very general "big case".
Almost convexity of the Mabuchi functional in singular settings
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