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arXiv · 1904.08145

On the umbilic set of immersed surfaces in three-dimensional space forms

Giovanni Catino·Alberto Roncoroni·Luigi Vezzoni
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Abstract

We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated Hopf theorem.

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Giovanni Catino, Alberto Roncoroni, Luigi Vezzoni. 2019-04-17. On the umbilic set of immersed surfaces in three-dimensional space forms. https://arxiv.org/abs/1904.08145

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