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.
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