Weingarten spheres in homogeneous three-manifolds

  1. Pablo Mira 1
  2. J.A. Gálvez
  1. 1 Universidad Politécnica de Cartagena

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

Geometric Analysis, Submanifolds, and Geometry of PDE's

Year of publication: 2019

Type: Conference paper


A classical theorem by H. Hopf shows that any compact constant mean curvature (CMC) surface of genus zero immersed in the Euclidean 3-space is a round sphere. This was generalized by Abresch and Rosenberg: any compact CMC surface of genus zero immersed in arotationally symmetric homogeneous three-manifold is a rotational sphere. In this talk we willpresent some wide generalizations of these results. In particular, we will show that any compactspecial Weingarten surface of genus zero immersed in the product space H2 × R is a rotationalsphere, and we will extend the Abresch-Rosenberg classification to the case of surfaces withconstant positive extrinsic curvature.