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Seminario di Equazioni Differenziali e Applicazioni: The Isometric Immersion Problem with Negative Gauss Curvature and Rough Data

Mercoledì 20 Maggio 2015, ore 12:15 - Aula 1BC45 - Cleopatra Christoforou

ARGOMENTI: Seminari

SEMINARIO DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Mercoledì 20 Maggio 2015 alle ore 12:15 in Aula 1BC45, Cleopatra Christoforou (University of Cyprus) terrà un seminario dal titolo "The Isometric Immersion Problem with Negative Gauss Curvature and Rough Data".

Abstract
We address the problem of global embedding of a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. A theorem of Efimov states that if the curvature decays too slowly to zero then global smooth immersion is impossible. On the other hand a theorem of J-X Hong shows that if decay is sufficiently rapid then global smooth immersion can be accomplished. In this talk, we present recent results on applying the methods from Continuum Physics to achieve a non-smooth global immersion with rough data and we give an emphasis on the role of decay rate of the Gauss curvature.

Rif. Int. M. Bardi, C. Marchi, L. Caravenna.

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