Diameter of K\"ahler currents
Differential Geometry
2023-11-01 v1 Complex Variables
Abstract
We establish upper bounds on the diameter of compact K\"ahler manifolds endowed with K\"ahler metrics whose volume form satisfies an Orlicz integrability condition. Our results extend previous estimates due to Fu-Guo-Song, Y.Li, and Guo-Phong-Song-Sturm. In particular, they do not involve any constraint on the vanishing of the volume form. Moreover, we show that singular K\"ahler-Einstein currents have finite diameter, provided that their local potentials are H\"older continuous.
Cite
@article{arxiv.2310.20482,
title = {Diameter of K\"ahler currents},
author = {Vincent Guedj and Henri Guenancia and Ahmed Zeriahi},
journal= {arXiv preprint arXiv:2310.20482},
year = {2023}
}
Comments
32 pages