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 …

There are several interesting examples of equations governing motion of hypersurfaces
bounding two phases of materials in various sciences. Such a hypersurface is called an …

The Lp-Minkowski problem introduced by Lutwak is solved for p⩾ n+ 1 in the smooth
category. The relevant Monge–Ampère equation (0.1) is solved for all p> 1. The same …

Although research in curve shortening flow has been very active for nearly 20 years, the
results of those efforts have remained scattered throughout the literature. For the first time …

Our main result shows the uniqueness of planar convex polygons of given outer orientations
to the sides and prescribed areas of the triangles formed by the origin with any two …

CLASSIFICATION OF LIMITING SHAPES FOR ISOTROPIC CURVE FLOWS 1. Introduction
Some natural parabolic deformations of convex curves Page 1 JOURNAL OF THE …

In image processing," motions by curvature" provide an efficient way to smooth curves
representing the boundaries of objects. In such a motion, each point of the curve moves, at …

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 …

In this paper we study the Lp-Minkowski problem for p=− n− 1, which corresponds to the
critical exponent in the Blaschke–Santalo inequality. We first obtain volume estimates for …

We interpret the log-Brunn–Minkowski conjecture of Böröczky–Lutwak–Yang–Zhang as a
spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert …