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MiS Preprint
70/2008

The Carnot-Caratheodory distance and the infinite Laplacian

Thomas Bieske, Federica Dragoni and Juan J. Manfredi

Abstract

In R^n equipped with the Euclidean metric, the distance from the origin is smooth and infinite harmonic everywhere except the origin. Using geodesics, we find a geometric characterization for when the distance from the origin in an arbitrary Carnot-Caratheodory space is a viscosity infinite harmonic function at a point outside the origin. We show that at points in the Heisenberg group and Grushin plane where this condition fails, the distance from the origin is not a viscosity infinite harmonic subsolution. In addition, the distance function is not a viscosity infinite harmonic supersolution at the origin.

Received:
Oct 20, 2008
Published:
Oct 27, 2008
MSC Codes:
53C17, 22E25, 35H20

Related publications

inJournal
2009 Repository Open Access
Thomas Bieske, Federica Dragoni and Juan J. Manfredi

The Carnot-Carathéodory distance and the infinite Laplacian

In: The journal of geometric analysis, 19 (2009) 4, pp. 737-754