Isoperimetric inequalities and monotonicity formulas for submanifolds in warped products manifolds

• Hilário Alencar ^[1] ; Gregório Silva Neto ^[1]
  1. [1] Universidade Federal de Alagoas

     Universidade Federal de Alagoas

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1821-1852
• Idioma: inglés
• DOI: 10.4171/rmi/1045
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• Resumen

  • In this paper we first prove some linear isoperimetric inequalities for submanifolds in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds. Moreover, the equality is attained. Next, we prove some monotonicity formulas for submanifolds with bounded mean curvature vector in warped product manifolds and, as consequences, we give lower bound estimates for the volume of these submanifolds in terms of the warping function. We conclude the paper with an isoperimetric inequality for minimal surfaces.