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Hypersurfaces with small extrinsic radius or large $\lambda_1$ in Euclidean spaces
Mean curvature Reilly inequality Laplacian Spectrum pinching results
2010/12/3
We prove that hypersurfaces of Rn+1 which are almost extremal for the
Reilly inequality on 1 and have Lp-bounded mean curvature (p > n) are Hausdorff close to a sphere, have almost constant mean cur...
The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes
Isoperimetric Profile Noncompact Riemannian Manifold for Small Volumes
2010/11/29
Let M be an n-dimensional Riemannian manifold. We deal, mainly, with the problem of finding a relatively compact domain D ⊂⊂ M that minimizes Area(∂D) among domains of the same volum...
Small Ball Probabilities for Smooth Gaussian fields and Tensor Products of Compact Operators
Small deviations slowly varying functions smooth covariances
2010/12/10
We find the logarithmic L2-small ball asymptotics for a class of zero mean Gaussian fields with covariances having the structure of “tensor product”. The main condition imposed on marginal covariances...