Complete self-shrinkers confined into some regions of the space
Differential Geometry
2018-11-14 v1
Abstract
We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is compact, we deduce spectral information on the natural drifted Laplacian associated to the self-shrinker. These results go in the direction of verifying the validity of a conjecture by H. D. Cao concerning the polynomial volume growth of complete self-shrinkers. A finite strong maximum principle in case the self-shrinker is confined into a cylindrical product is also presented.
Keywords
Cite
@article{arxiv.1212.4041,
title = {Complete self-shrinkers confined into some regions of the space},
author = {Stefano Pigola and Michele Rimoldi},
journal= {arXiv preprint arXiv:1212.4041},
year = {2018}
}
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21 pages