English

Moser-Trudinger inequalities and complex Monge-Ampere equation

Complex Variables 2023-08-01 v3 Analysis of PDEs

Abstract

Our aim is to give a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, our result already gives a new Moser-Trudinger inequality for functions in the Sobolev space W1,2W^{1,2} of a domain in R2R^2. We also deduce a new necessary condition for the complex Monge-Ampere equation for a given measure on a compact Kahler manifold to admit a Holder continuous solution.

Keywords

Cite

@article{arxiv.2006.07979,
  title  = {Moser-Trudinger inequalities and complex Monge-Ampere equation},
  author = {Tien-Cuong Dinh and George Marinescu and Duc-Viet Vu},
  journal= {arXiv preprint arXiv:2006.07979},
  year   = {2023}
}

Comments

Final version, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)

R2 v1 2026-06-23T16:18:57.363Z