# Umbilicity and characterization of Pansu spheres in the Heisenberg group

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Jih-Hsin Cheng , Academia Sinica, Taiwan
Fine Hall 314

For n≥2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group H_{n}. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p(or horizontal)-mean curvature in H_{n} up to Heisenberg translations. This is joint work with Hung-Lin Chiu, Jenn-Fang Hwang, and Paul Yang.