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Splitting of 3-Manifolds and Rigidity of Area-Minimising Surfaces
Rigidity of Area-Minimising Surfaces Splitting of 3-Manifolds Differential Geometry
2011/9/21
Abstract: In this paper we prove an area comparison result for certain totally geodesic surfaces in 3-manifolds with a lower bound on the scalar curvature. This result is a variant of a comparison the...
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
homogeneous solutions Yamabe problem spheres Differential Geometry
2011/9/21
Abstract: We study existence and non existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all ...
Rigidity of high dimensional graph manifolds
Quasi-isometry quasi-action graph of groups CAT(0) space Borel conjecture Baum-Connes conjecture
2011/9/1
Abstract: We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the produc...