The Weyl problem for unbounded convex surfaces in H^3

Abstract: The classical Weyl problem in Euclidean space, solved in the 1950s, askswhether any smooth metric of positive curvature on the sphere can be realized as the induced metric on the boundary of a unique convex subset in $\R^3$. It was extended by Alexandrov to the hyperbolic space, where a dual problem can also be considered: prescribing the third fundamental form of a convex surface.

We will describe extensions of the Weyl problem and its dual to unbounded convex surfaces in $H^3$. Two types of generalizations can be stated, one concerning unbounded convex surfaces, the other unbounded locally convex surfaces. Both questions have as special cases a number of known result or conjectures concerning 3-dimensional hyperbolic geometry, circle packings, etc. We will present a rather general existence result concerning convex subsets.

differential geometry

Audience: researchers in the topic

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

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