Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics

By Robert J. Berman, B. Berndtsson. 2014

167 citations recorded by the source corpus.

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a proof of the uniqueness of constant scalar curvature metrics (or more generally extremal metrics) modulo automorphisms. The key ingredient is a new local positivity property of weak solutions to the homogenuous Monge-Ampere equation on a product domain, whose proof uses plurisubharmonic variation of Bergman kernels.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/03787a5771b5ffc306029c1de821a2d40b1da12b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Abdellah Lahdili
2. Jiyuan Han
3. Chi Li

In Geometry and Topology

1. Abdellah Lahdili
2. Jiyuan Han
3. Chi Li

Citations in the corpus

• Kähler metrics with constant weighted scalar curvature and weighted K‐stability (2018, methodology): “Let φ0, φ1 ∈ KT ω be two smooth Kähler potentials and φt the weak geodesic connecting φ0 and φ1 (see [11, 22] and the references therein for the definition of a weak geodesic).”