Calculus of Variations and Geometric Measure Theory

F. Dragoni - J. Manfredi - D. Vittone

Weak Fubini Property and infinity Harmonic Functions in Riemannian and Sub-Riemannian Manifolds

created by vittone on 05 May 2010
modified on 28 Nov 2012


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


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