English

Isoperimetric inequality under K\"ahler Ricci flow

Differential Geometry 2013-07-11 v3

Abstract

Let (\M,g(t))({\M}, g(t)) be a K\"ahler Ricci flow with positive first Chern class. We prove a uniform isoperimetric inequality for all time. In the process we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on (\M,g(t))({\M}, g(t)), and a Poincar\'e inequality without assuming the Ricci curvature is bounded from below.

Keywords

Cite

@article{arxiv.1203.1400,
  title  = {Isoperimetric inequality under K\"ahler Ricci flow},
  author = {Gang Tian and Qi S. Zhang},
  journal= {arXiv preprint arXiv:1203.1400},
  year   = {2013}
}

Comments

final version, to appear in Am. J. Math