In this paper we study non-compact self-shrinkers first in general codimension and then in codimension 1. We respectively prove some vanishing theorems giving rise to rigidity of the self-shrinker and then estimates involving the higher order mean curvatures for the oriented case. The paper ends with some results on their index when considered as appropriate -minimal hypersurfaces.

Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers / G.P. Bessa, L.F. Pessoa, M. Rigoli. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 226:2(2018), pp. 703-736. [10.1007/s11856-018-1703-3]

Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers

M. Rigoli
2018

Abstract

In this paper we study non-compact self-shrinkers first in general codimension and then in codimension 1. We respectively prove some vanishing theorems giving rise to rigidity of the self-shrinker and then estimates involving the higher order mean curvatures for the oriented case. The paper ends with some results on their index when considered as appropriate -minimal hypersurfaces.
Mathematics (all)
Settore MAT/05 - Analisi Matematica
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/621399
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