MATH Seminar

Title: Souls of some convex surfaces
Seminar: Analysis and Differential Geometry
Speaker: Eric Choi of Emory University
Contact: Eric Choi, echoi7@emory.edu
Date: 2011-03-01 at 4:00PM
Venue: MSC W301
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Abstract: The $soul$ of a complete, noncompact, connected Riemannian manifold $(M, g)$ of nonnegative sectional curvature is a compact, totally convex, totally geodesic submanifold such that $M$ is diffeomorphic to the normal bundle of the soul. Hence, understanding of the souls of $M$ can reduce the study of $M$ to the study of a compact set. Also, souls are metric invariants, so understanding how they behave under deformations of the metric is useful to analyzing the space of metrics on $M$. In particular, little is understood about the case when $M = R^2$. Convex surfaces of revolution in $R^3$ are one class of two-dimensional Riemannian manifolds of nonnegative sectional curvature, and I will discuss some results regarding the sets of souls for some of such convex surfaces. % r_h(sis $c = r \sin \phi,$ where $\phi = \angle (\dot \g(t), \dot \sigma)$ ($\sigma$ is the meridian through $\g(t)$.). %the intervals for integration must be broken up as follows: $[r(s_1), r(s_0)), [r(s_0,$