Geometric pluripotential theory on Kähler manifolds

By Tam'as Darvas. Advances in Complex Geometry, 2019

68 citations recorded by the source corpus.

Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively turning the variational problems in question into problems of infinite dimensional convex optimization, yielding existence results for solutions of the underlying complex Monge-Amp\`ere equations. The purpose of this survey is to describe these developments from basic principles.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/798d6ca56a8bf99d608da1945b3343bb860de735

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

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Regularity of weak minimizers of the K-energy and applications to properness and K-stability (2016, methodology): “For details on this we refer the interested reader to the original papers, as well as the comprehensive recent survey [Da3, Chapter 3].”