Complex Monge-Ampere equations with solutions in finite energy classes
Do Duc Thai, Duc-Viet Vu
TL;DR
This paper characterizes probability measures on compact Kähler manifolds for which the Monge-Ampère equation admits solutions with finite energy, extending results to big cohomology classes.
Contribution
It provides a complete characterization of measures leading to finite energy solutions of Monge-Ampère equations, including in big cohomology classes.
Findings
Characterization of measures with finite energy solutions
Extension of results to big cohomology classes
Conditions for existence of solutions in finite energy classes
Abstract
We characterize the class of probability measures on a compact Kahler manifold such that the associated Monge-Amp\`ere equation has a solution of finite pluricomplex energy. Our results are also valid in the big cohomology class setting.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows