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Mathematics > Differential Geometry

arXiv:1804.09076 (math)
[Submitted on 24 Apr 2018 (v1), last revised 21 Jul 2018 (this version, v2)]

Title:Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flow

Authors:Jacob Bernstein, Lu Wang
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Abstract:We show compactness in the locally smooth topology for certain natural families of asymptotically conical self-expanding solutions of mean curvature flow. Specifically, we show such compactness for the set of all two-dimensional self-expanders of a fixed topological type and, in all dimensions, for the set of self-expanders of low entropy and for the set of mean convex self-expanders with strictly mean convex asymptotic cones. From this we deduce that the natural projection map from the space of parameterizations of asymptotically conical self-expanders to the space of parameterizations of the asymptotic cones is proper for these classes.
Comments: 19 pages, 0 figures, fix minor typos and update references
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
MSC classes: 53C44
Cite as: arXiv:1804.09076 [math.DG]
  (or arXiv:1804.09076v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1804.09076

Submission history

From: Lu Wang [view email]
[v1] Tue, 24 Apr 2018 14:53:33 UTC (22 KB)
[v2] Sat, 21 Jul 2018 18:18:29 UTC (22 KB)
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