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 …

We consider a class of fully nonlinear parabolic evolution equations for hypersurfaces in
Euclidean space. A new geometrical lemma is used to prove that any strictly convex …

We consider the behaviour of convex curves undergoing curvature-driven motion. In
particular we describe the long-term behaviour of solutions and properties of limiting …

We prove that convex hypersurfaces in R n+ 1 contracting under the flow by any power α> 1
n+ 2 of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a …

We prove uniform regularity estimates for the normalized Gauss curvature flow in higher
dimensions. The convergence of solutions in C∞-topology to a smooth strictly convex …

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

We consider compact convex hypersurfaces contracting by functions of their curvature.
Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to …

The aim of this article is to give an introduction to certain inequalities named after Carl
Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions …

Convex ancient solutions to curve shortening flow | SpringerLink Skip to main content
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Ancient mean curvature flows out of polytopes Page 1 GGG G G G G GGGG G G G GGG
TTT T T T TTTTTT T T T T T Geometry & Topology msp Volume 26 (2022) Ancient mean …