Smoczyk, K.: Self-Expanders of the Mean Curvature Flow. In: Vietnam Journal of Mathematics 49 (2021), Nr. 2, S. 433-445. DOI: https://doi.org/10.1007/s10013-020-00469-1
Abstract: | |
We study self-expanding solutions Mm⊂ ℝn of the mean curvature flow. One of our main results is, that complete mean convex self-expanding hypersurfaces are products of self-expanding curves and flat subspaces, if and only if the function |A|2/|H|2 attains a local maximum, where A denotes the second fundamental form and H the mean curvature vector of M. If the principal normal ξ = H/|H| is parallel in the normal bundle, then a similar result holds in higher codimension for the function |Aξ|2/|H|2, where Aξ is the second fundamental form with respect to ξ. As a corollary we obtain that complete mean convex self-expanders attain strictly positive scalar curvature, if they are smoothly asymptotic to cones of non-negative scalar curvature. In particular, in dimension 2 any mean convex self-expander that is asymptotic to a cone must be strictly convex. | |
License of this version: | CC BY 4.0 Unported |
Document Type: | Article |
Publishing status: | publishedVersion |
Issue Date: | 2021 |
Appears in Collections: | Fakultät für Mathematik und Physik |
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