Gap theorems for complete self-shrinkers of $r$-mean curvature flows
Differential Geometry
2024-04-02 v2 Analysis of PDEs
Abstract
In this paper, we prove gap results for complete self-shrinkers of the -mean curvature flow involving a modified second fundamental form. These results extend previous results for self-shrinkers of the mean curvature flow due to Cao-Li and Cheng-Peng. To prove our results we show that, under suitable curvature bounds, proper self-shrinkers are parabolic for a certain second-order differential operator which generalizes the drifted Laplacian and, even if is not proper, this differential operator satisfies an Omori-Yau type maximum principle.
Keywords
Cite
@article{arxiv.2402.09627,
title = {Gap theorems for complete self-shrinkers of $r$-mean curvature flows},
author = {Hilário Alencar and G. Pacelli Bessa and Gregório Silva Neto},
journal= {arXiv preprint arXiv:2402.09627},
year = {2024}
}
Comments
22 pages. In this new version, the presentation and proof of Lemma 3.1 have been simplified, and some typos have been corrected. The main results remain unchanged