Revista Matemática Iberoamericana


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Volume 34, Issue 4, 2018, pp. 1821–1852
DOI: 10.4171/rmi/1045

Published online: 2018-12-06

Isoperimetric inequalities and monotonicity formulas for submanifolds in warped products manifolds

Hilário Alencar[1] and Gregório Silva Neto[2]

(1) Universidade Federal de Alagoas, Maceió, Brazil
(2) Universidade Federal de Alagoas, Maceió, Brazil

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.

Keywords: Warped product, isoperimetric inequality, monotonicity formula

Alencar Hilário, Silva Neto Gregório: Isoperimetric inequalities and monotonicity formulas for submanifolds in warped products manifolds. Rev. Mat. Iberoam. 34 (2018), 1821-1852. doi: 10.4171/rmi/1045