Isoperimetric inequality under Kähler Ricci flow

Abstract

Let $({\M}, g(t))$ be a Kähler 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 $({\M}, g(t))$, and a Poincaré inequality without assuming the Ricci curvature is bounded from below.

final version, to appear in Am. J. Math

References in corpus (3)

• The logarithmic Sobolev inequality along the Ricci flow
• Space of Ricci flows (II)
• Convergence of a Kähler-Ricci flow

Cited by in corpus (1)

• Space of Ricci flows (II)