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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds
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by Federica Dragoni, Juan J. Manfredi and Davide Vittone PDF
Trans. Amer. Math. Soc. 365 (2013), 837-859 Request permission


We examine the relationship between infinity harmonic functions, absolutely minimizing Lipschitz extensions, strong absolutely minimizing Lipschitz extensions, and absolutely gradient minimizing extensions in Carnot-Carathéodory spaces. Using the weak Fubini property we show that absolutely minimizing Lipschitz extensions are infinity harmonic in any sub-Riemannian manifold.
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Additional Information
  • Federica Dragoni
  • Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, Wales, United Kingdom CF24 4AG
  • Juan J. Manfredi
  • Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • MR Author ID: 205679
  • Davide Vittone
  • Affiliation: Dipartimento di Matematica, University of Padova, via Trieste 63, 35121 Padova, Italy
  • Received by editor(s): December 15, 2010
  • Received by editor(s) in revised form: April 22, 2011
  • Published electronically: September 19, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 837-859
  • MSC (2010): Primary 53C17, 22E25, 35H20, 53C22
  • DOI:
  • MathSciNet review: 2995375