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Non-existence of strictly monotone vector fields on certain Riemannian manifolds

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Abstract

The main goal of this paper is to prove that Riemannian manifolds that admit monotone vector fields that satisfy a weaker condition than strictly monotone has infinite volume, in a sense, generalizing a result that Bishop and O’Neill proved for convex functions.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Piauí, 64049-550, Ininga, Teresina, PI, Brazil

    J. X. Cruz Neto, I. D. Melo & P. A. Sousa

Authors
  1. J. X. Cruz Neto
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  2. I. D. Melo
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  3. P. A. Sousa
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Corresponding author

Correspondence to J. X. Cruz Neto.

Additional information

The first author is supported by CNPq/Brazil. The third author is supported by CNPq/Brazil and PROCAD/CAPES/Brazil.

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Cruz Neto, J.X., Melo, I.D. & Sousa, P.A. Non-existence of strictly monotone vector fields on certain Riemannian manifolds. Acta Math. Hungar. 146, 240–246 (2015). https://doi.org/10.1007/s10474-015-0482-0

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  • DOI: https://doi.org/10.1007/s10474-015-0482-0

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