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Boundary rigidity of two-dimensional strongly geodesic minimizing (SGM) manifolds

Prof. Leonid N. Pestov, Immanuel Kant Baltic Federal University
Speaker
Prof. Leonid N. Pestov, Immanuel Kant Baltic Federal University
When Jan 20, 2017
from 04:00 PM to 05:00 PM
Where LH006
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Abstract

Let (M, g) be a smooth compact Riemannian manifold with boundary and let dg be the boundary distance function. The Boundary Rigidity problem is the problem about injectivity of the map g → dg (up to a natural obstruction). There are some examples of boundary rigid manifolds (flat metric – M. Gromov, two-dimensional manifolds of non-positive curvature – C. Croke, manifolds with metric, close to flat metric – D.Burago & S.Ivanov, two-dimensional simple manifolds – L.N. Pestov & G.Uhlmann). Here we generalize the last result for two-dimensional SGM manifolds.

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