Gap theorems for complete self-shrinkers of $r$-mean curvature flows

Autor:	Alencar, Hilário, Bessa, G. Pacelli, Neto, Gregório Silva
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs 53E10 53C42 53E40 53C21
Druh dokumentu:	Working Paper
Popis:	In this paper, we prove gap results for complete self-shrinkers of the $r$-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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.09627 Zobrazit plný text záznamu View this record from Arxiv