DIFFERENTIAL GEOMETRY/PDE SEMINAR

Tuesday, November 25, 2003 Padelford C-36 1:30 pm (Note: special day)

Bi-Lipschitz Equivalence of Alexandrov Surfaces of Bounded Total Curvature

Yuri Burago (Steklov Institute, St.Petersburg)

I will discuss the following problems: (1) Under what conditions are two Alexandrov surfaces of bounded total curvature bi-Lipschitz equivalent; and (2) Upon which characteristics of the surfaces does the bi-Lipschitz constant depends on. Our solution of the second problem is new even in the Riemannian manifolds category. Note, that in contrast to hyperbolic spaces, the spaces of bounded total curvature usually are “almost flat” at infinity. Thus the set-up does not seem to be related to large scale geometry. These problems are inspired by a recent paper by M. Bonk and U. Lang, who have found a (sharp, at least in some sense) bi-Lipschitz constant for surfaces (of total curvature less than 2π) homeomorphic to the plane. I don’t expect from my audience any knowledge of the theory of Alexandrov spaces.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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