Published Paper
Inserted: 5 may 2010
Last Updated: 28 nov 2012
Journal: Trans. Amer. Math. Soc.
Volume: 365
Number: 2
Pages: 837-859
Year: 2013
Doi: 10.1090/S0002-9947-2012-05612-1
Notes:
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.
Keywords: Carnot-Carathéodory spaces, Absolutely minimizing Lipschitz extension, Infinity Laplacian, Riemannian manifolds
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