The Carnot-Carathéodory Distance and the Infinite Laplacian

Bieske, T., Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725 and Manfredi, J. J. 2009. The Carnot-Carathéodory Distance and the Infinite Laplacian. Journal of Geometric Analysis 19 (4) , pp. 737-754. 10.1007/s12220-009-9087-6

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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-Carathéodory 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Carnot-Carathéodory spaces - Infinite Laplacian - Viscosity solutions
Publisher:	Springer
ISSN:	1050-6926
Last Modified:	18 Oct 2022 13:26
URI:	https://orca.cardiff.ac.uk/id/eprint/13889

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