Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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