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Riemannian manifolds with boundary and smooth domains
Stefano Pigola (Insubria)
Aula Beltrami - Giovedì 3 Novembre 2016 h.16:00
Abstract. The most natural way to visualize a Riemannian manifold with boundary is to consider it as a smooth, proper domain inside a Riemannian manifold without boundary. The extent to which this picture represents the general situation, when geodesic completeness and curvature bounds are imposed on the ambient, is an interesting problem and may help the geometric analysis on the original space. In the opposite direction, sometimes it is useful to think of a smooth domain as an independent manifold with boundary. This is the case, for instance, when we study a Liouville type property whose validity depends on geometric conditions localized on a portion of the space. In this talk I will discuss the extension problem for Riemannian manifolds and, if time permits, I will present some aspects related to the second direction.
Università degli Studi di Pavia -
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