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Generalizations of the Liouville theorem

Ranjbar-Motlagh, A ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.difgeo.2007.11.026
  3. Publisher: 2008
  4. Abstract:
  5. The purpose of this paper is to generalize the Liouville theorem for functions which are defined on the complete Riemannian manifolds. Then, we apply it to the isometric immersions between complete Riemannian manifolds in order to obtain an estimate for the size of the image of immersions in terms of the supremum of the length of their mean curvature vector in a quite general setting. The proofs are based on the Calabi's generalization of maximum principle for functions which are not necessarily differentiable. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Isometric immersion ; Mean curvature ; Laplacian ; Generalized maximum principle ; Generalized Liouville theorem
  8. Source: Differential Geometry and its Application ; Volume 26, Issue 3 , 2008 , Pages 339-345 ; 09262245 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0926224507001015