Isoperimetric inequality under Kähler Ricci flow

Details Isoperimetric inequality under Kähler Ricci flow Isoperimetric inequality under Kähler Ricci flow

2012-03-07

arxiv.org/abs/1203.1400v2

Mathematics

Differential Geometry

One remark on p16 is added, which shows a scaling invariant integral bound for Ricci curvature

Scientific paper

Let $({\M}, g(t))$ be a K\"ahler Ricci flow with positive first Chern class. First, we prove a uniform isoperimetric inequality for all time. Second it is shown that the Ricci potential is in the class $C^{1, \alpha}(B)$ when the ball $B$ is within a coordinate chart. Here $\alpha$ is any positive number less than 1. We also prove a Cheng-Yau type log gradient bound for positive harmonic functions on $({\M}, g(t))$ without assuming the Ricci curvature is bounded from below.

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