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Volume growth, “a priori” estimates, and geometric applications

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Abstract

We obtain a maximum principle, and “a priori” upper estimates for solutions of a class of non-linear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumption of volume growth conditions. Various applications of the results obtained are presented.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133, Milano, Italy

    Stefano Pigola

  2. Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Università dell’Insubria - Como, via Valleggio 11, 22100, Como, Italy

    Marco Rigoli & Alberto G. Setti

Authors
  1. Stefano Pigola
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  2. Marco Rigoli
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  3. Alberto G. Setti
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Correspondence to Stefano Pigola.

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Pigola, S., Rigoli, M. & Setti, A. Volume growth, “a priori” estimates, and geometric applications. Geom. funct. anal. 13, 1302–1328 (2003). https://doi.org/10.1007/s00039-003-0447-2

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  • DOI: https://doi.org/10.1007/s00039-003-0447-2

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