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Quantum ergodicity for restrictions to hypersurfaces
Quantum ergodicity restrictions hypersurfaces Analysis of PDEs
2012/4/17
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in t...
The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Hypersurfaces with constant mean curvature Rigidity Scalar curvature Clifford torus
2011/1/20
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng-Terng, Wei-Xu, Zhang, and Ding-Xin to the case of hypersurfaces with small constant mean curvature. Let Mn b...
Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature
Compact Mean Convex Hypersurfaces Fundamental Group of Manifolds Nonnegative Ricci Curvature
2011/1/19
We show that the existence of an embedded compact, boundaryless hypersurface S of strictly
positive mean curvature in a noncompact, connected, complete Riemannian n-manifold N of non-
negative Ricci...
Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Carnot groups Sub-Riemannian Geometry Hypersurfaces Isoperimetric Inequality
2011/1/20
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Our main result is an isoperimetric inequality for the case of a C2-smooth compact hype...