Diameter estimates in K\"ahler geometry
Differential Geometry
2022-09-21 v1 Analysis of PDEs
Metric Geometry
Abstract
Diameter estimates for K\"ahler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for estimates for the Monge-Amp\`ere equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the K\"ahler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.
Keywords
Cite
@article{arxiv.2209.09428,
title = {Diameter estimates in K\"ahler geometry},
author = {Bin Guo and Duong H. Phong and Jian Song and Jacob Sturm},
journal= {arXiv preprint arXiv:2209.09428},
year = {2022}
}