Properties of infinite harmonic functions relative to Riemannian vector fields

  • Thomas Bieske University of South Florida
Keywords: Viscosity solutions, Riemannian vector fields, Infinite Laplacian


We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of infinite harmonic functions in Riemannian spaces. We then show such functions are equivalent to those that enjoy comparison with Riemannian cones. Using comparison with cones, we show that the Riemannian distance is a supersolution to the infinite Laplace equation, but is not necessarily a solution. We find some geometric conditions under which the Riemannian distance is infinite harmonic and under which it fails to be infinite harmonic.

Author Biography

Thomas Bieske, University of South Florida
Department of Mathematics
Tampa, FL 33620, USA