Archivio Istituzionale della RicercaIn this paper we show that the only properly immersed self-shrinkers Σin Rm+1with Morse index 1are the hyperplanes through the origin. Moreover, we prove that if Σis not a hyperplane through the origin then the index jumps and it is at least m +2, with equality if and only if Σis a cylinder Rm−k×Sk(√k)for some 1 ≤k≤m −1
Rigidity and gap results for low index properly immersed self-shrinkers in Rm+1 / Impera, Debora. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - STAMPA. - 64:(2019), pp. 1-12. [10.1016/j.difgeo.2019.01.003]
Rigidity and gap results for low index properly immersed self-shrinkers in Rm+1
Impera, Debora
2019
Abstract
In this paper we show that the only properly immersed self-shrinkers Σin Rm+1with Morse index 1are the hyperplanes through the origin. Moreover, we prove that if Σis not a hyperplane through the origin then the index jumps and it is at least m +2, with equality if and only if Σis a cylinder Rm−k×Sk(√k)for some 1 ≤k≤m −1
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11583/2766632