Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds.
This book is an introduction to Ricci flow for graduate students and mathematicians …

DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH
POTENTIALS **aodong Cao and Richard S. Hamilton 1 Introduc Page 1 DIFFERENTIAL …

In this paper, we consider orthogonal Ricci curvature Ric^ ⊥ R ic⊥ for Kähler manifolds,
which is a curvature condition closely related to Ricci curvature and holomorphic sectional …

Abstract We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat
equation and the backward conjugate heat equation, both coupled with the Ricci flow. We …

Abstract We prove Li–Yau type gradient bounds for the heat equation either on manifolds
with fixed metric or under the Ricci flow. In the former case the curvature condition is| R …

Let $(\mathbf {M}^ n, g_ {ij}) $ be a complete Riemannian manifold. For any constants $ p,\r>
0$, define $\displaystyle k (p, r)=\sup _ {x\in M} r^ 2\left (\oint _ {B (x, r)}| Ric^-|^ p …

The first part of this paper is devoted to proving a comparison theorem for Kähler manifolds
with holomorphic bisectional curvature bounded from below. The model spaces being …

In this paper, we derive a general evolution formula for possible Harnack quantities. As a
consequence, we prove several differential Harnack inequalities for positive solutions of …

In this paper we prove a new matrix Li-Yau-Hamilton (LYH) estimate for Kähler-Ricci flow on
manifolds with nonnegative bisectional curvature. The form of this new LYH estimate is …

In this work, optimal rigidity results for eigenvalues on Kähler manifolds with positive Ricci
lower bound are established. More precisely, for those Kähler manifolds whose first …