Slab theorem and halfspace theorem for constant mean curvature surfaces in H2 R

• Laurent Hauswirth ^[3] ; Ana Menezes ^[1] ; Magdalena Rodríguez ^[2]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] Universidad de Granada

     Universidad de Granada

     Granada, España

     
  3. [3] Université Gustave Eiffel; and Université Paris-Est Créteil, Marne-la-Vallée

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 1, 2023, págs. 307-320
• Idioma: inglés
• DOI: 10.4171/RMI/1372
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• Resumen

  • We prove that a properly embedded annular end of a surface in H2 R with constant mean curvature 0 < H 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H 1=2 contained in H2 Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H2 . For the case H D 1=2, the graph is entire.