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arXiv · 2402.09627

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

Hilário Alencar·G. Pacelli Bessa·Gregório Silva Neto
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Abstract

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.

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BibTeXRIS

Hilário Alencar, G. Pacelli Bessa, Gregório Silva Neto. 2024-02-15. Gap theorems for complete self-shrinkers of $r$-mean curvature flows. https://arxiv.org/abs/2402.09627

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