Complete self-shrinkers confined into some regions of the space |
| |
Authors: | Stefano Pigola Michele Rimoldi |
| |
Affiliation: | 1. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100, Como, Italy
|
| |
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: | |
本文献已被 SpringerLink 等数据库收录! |
|