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Constant Nonlocal Mean Curvature Hypersurfaces

Mouhamed Moustapha Fall
AIMS, Senegal
Friday, December 6, 2019 - 10:00
Luigi Stasi Seminar Room, ICTP

The notion of Nonlocal Mean Curvature (NMC) appeared in the mathematics literature around 10 years ago. It arises in variational problems for the fractional perimeter and related nonlocal interfacial energies. I will first review the notion of NMC and discuss its main properties in comparison with the classical mean curvature.  I will also focus on the class of hypersurfaces with constant NMC. Although this class is still largely unexplored, first results show both similarities and striking differences to the classical local setting of constant mean curvature surfaces. [Joint work with: Xavier Cabré (Universitat Politècnica de Catalunya, Barcelona), Joan Solà-Morales (Universitat Politècnica de Catalunya, Barcelona), Tobias Weth (Goethe-University Frankfurt)]

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