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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds


Authors: Federica Dragoni, Juan J. Manfredi and Davide Vittone
Journal: Trans. Amer. Math. Soc. 365 (2013), 837-859
MSC (2010): Primary 53C17, 22E25, 35H20, 53C22
Published electronically: September 19, 2012
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Abstract: 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

Davide Vittone
Affiliation: Dipartimento di Matematica, University of Padova, via Trieste 63, 35121 Padova, Italy

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05612-1
PII: S 0002-9947(2012)05612-1
Keywords: Absolutely minimizing Lipschitz extension, infinity Laplace equation, Riemannian manifolds, Carnot-Carathéodory spaces
Received by editor(s): December 15, 2010
Received by editor(s) in revised form: April 22, 2011
Published electronically: September 19, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.