English

Diameter estimates in K\"ahler geometry II: removing the small degeneracy assumption

Differential Geometry 2024-05-29 v1 Analysis of PDEs Complex Variables

Abstract

In this short note, we remove the small degeneracy assumption in our earlier works [10, 11]. This is achieved by a technical improvement of Corollary 5.1 in [10]. As a consequence, we establish the same geometric estimates for diameter, Green's functions and Sobolev inequalities under an entropy bound for the K\"ahler metrics, without any small degeneracy assumption.

Keywords

Cite

@article{arxiv.2405.18280,
  title  = {Diameter estimates in K\"ahler geometry II: removing the small degeneracy assumption},
  author = {Bin Guo and Duong H. Phong and Jian Song and Jacob Sturm},
  journal= {arXiv preprint arXiv:2405.18280},
  year   = {2024}
}