Results 11 to 20 of about 101,246 (190)
Ancient solutions of geometric flows with curvature pinching
Journal of Geometric Analysis, 2018 We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean ...
Risa, Susanna, Sinestrari, Carlo
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Minimal cones and self-expanding solutions for mean curvature flows
Mathematische Annalen, 2019 In this paper, we study self-expanding solutions for mean curvature flows and their relationship to minimal cones in Euclidean space. In [18], Ilmanen proved the existence of self-expanding hypersurfaces with prescribed tangent cones at infinity.
Ding, Qi
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Convergence of nonlocal geometric flows to anisotropic mean curvature motion [PDF]
, 2018 We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blow-up limit from them.
Cesaroni, Annalisa, Pagliari, Valerio
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Parabolic theory as a high-dimensional limit of elliptic theory [PDF]
, 2017 The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity theory of ...
Davey, Blair
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Level set approach for fractional mean curvature flows [PDF]
, 2009 This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set.
Imbert, Cyril
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A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
, 2017 Entanglement entropies are notoriously difficult to compute. Large-N strongly-coupled holographic CFTs are an important exception, where the AdS/CFT dictionary gives the entanglement entropy of a CFT region in terms of the area of an extremal bulk ...
Fischetti, Sebastian, Wiseman, Toby
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Dirichlet sigma models and mean curvature flow
, 2007 The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional,
A. Adams +52 more
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Topological Change in Mean Convex Mean Curvature Flow
, 2013 Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if ...
A. Hatcher +11 more
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An application of dual convex bodies to the inverse Gauss curvature flow
, 2014 By means of dual convex bodies, we obtain regularity of solutions to the expanding Gauss curvature flows with homogeneity degrees $-p ...
Ivaki, Mohammad N.
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Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow
, 2018 Let $M\subset {\mathbf R}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\rm th}$ homology. We show that the entropy of $M$ is greater than or equal to the entropy of a round $k$-sphere, and that ...
Hershkovits, Or, White, Brian
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