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Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Differential Geometry Seminar
and
Geometry, Topology, and Physics Seminar
Cross Curvature Flow on
Locally Homogenous Three-manifolds
Xiaodong Cao
MSRI and Cornell University
Friday, April 20, 2007, 3:30 p.m.
Room 6635 South Hall
Abstract: Recently, Chow and Hamilton introduced the cross curvature flow on
three-manifolds, which is a weakly parabolic partial differential equation system when
the sectional curvatures have a definite sign. They also conjectured the long time
existence and convergence of cross curvature flow on closed three-manifolds with
negative sectional curvature. In this talk, we will study the cross curvature flow
on locally homogenous three-manifolds. We will describe the long time behavior of
the cross curvature flow for each case. This is a joint work with Yilong Ni and Laurent
Saloff-Coste.
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