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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.
