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math.DG2019
On the umbilic set of immersed surfaces in three-dimensional space forms
Giovanni Catino, Alberto Roncoroni, Luigi Vezzoni
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a -dimensional space form has positive measure. In case of an im…
math.DG2018
Quantitative stability for hypersurfaces with almost constant curvature in space forms
Giulio Ciraolo, Alberto Roncoroni, Luigi Vezzoni
The Alexandrov Soap Bubble Theorem asserts that the distance spheres are the only embedded closed connected hypersurfaces in space forms having constant mean curvature. The theorem…