|Registration Deadline:||October 23, 2010 over 2 years ago|
- Mohammad Ghomi (Georgia Institute of Technology)
Title: Tangent cones and regularity of real hypersurfaces
Abstract: We characterize C^1 embedded hypersurfaces of R^n as the only locally closed sets with continuously varying flat tangent cones whose measure-theoretic-multiplicity is at most m < 3/2. It follows then that any (topological) hypersurface which has flat tangent cones and is supported everywhere by balls of uniform radius is C^1. In the real analytic case the same conclusion holds under the weakened hypothesis that each tangent cone be a hypersurface. In particular, any convex real analytic hypersurface X of R^n is C^1. Furthermore, if X is real algebraic, strictly convex, and unbounded then its projective closure is a C^1 hypersurface as well, which shows that X is the graph of a function defined over an entire hyperplane. Finally, the optimality of these results will be demonstrated by means of a number of examples. This is joint work with Ralph Howard.
- Christopher B. Croke (University of Pennsylvania)
Title: Examples of Riemannian metrics on spheres
Abstract: In this talk we discuss some interesting examples of metrics on spheres. On the two sphere we construct (with Balacheff and Katz) metrics of Zoll type where L>2D relating the diameter D and the least length L of a nontrivial closed geodesic. This gives a counterexample to a conjecture of Nabutovsky and Rotman. The construction relies on Guillemin's theorem concerning the existence of Zoll surfaces integrating an arbitrary infinitesimal odd deformation of the round metric. We conclude that the round metric is not even locally optimal for the ratio L/D. For n>2 we give easy examples of metrics on the n-sphere with arbitrarily small volume and where the distance between any pair of antipodal points is greater than 1. This answers a question of Berger.
- John Lott (University of California, Berkeley)
Title: Geometrization of orbifolds via Ricci flow
Abstract : A three-dimensional compact orbifold (with no bad suborbifolds) is known to have a geometric decomposition from the work of Perelman along with earlier work of Boileau-Leeb-Porti/Cooper-Hodgson-Kerckhoff. I'll describe a unified proof of the geometrization of orbifolds, using Ricci flow. The emphasis will be on the aspects that are particular to orbifolds. This is joint work with Bruce Kleiner.
10:00am Coffee & Refreshments
11:00am Mohammad Ghomi
1:45pm Organizational Meeting
2:00pm Christopher B. Croke
3:00pm Coffee & Refreshments
3:30pm John Lott
5:30pm Dinner at the home of David Hoffman
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A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.
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