Calculus of Variations and Geometric Measure Theory
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G. Catino - A. Roncoroni - L. Vezzoni

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

created by catino on 17 Apr 2019


Submitted Paper

Inserted: 17 apr 2019
Last Updated: 17 apr 2019

Year: 2019


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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