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arXiv · 2012.07104

Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set

Hilário Alencar·Manuel Cruz·Gregório Silva Neto
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Abstract

In this paper we prove rigidity results for the sphere, the plane and the right circular cylinder as the only self-shrinkers satisfying a classic geometric assumption, namely the union of all tangent affine submanifolds of a complete self-shrinker omits a non-empty set of the Euclidean space. This assumption lead us to a new class of submanifolds, different from those with polynomial volume growth or the proper ones. We also prove an analogous result for self-expanders.

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Hilário Alencar, Manuel Cruz, Gregório Silva Neto. 2020-12-13. Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set. https://doi.org/10.1007/s00025-023-01909-3

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