University of Cincinnati
Geometric and Analytic Aspects of ∞-Poincare´ Inequalities
ABSTRACT: The study of absolute minimizing Lipschitz extensions and infinity-harmonic functions in the Euclidean setting was initiated by Aronsson, Crandall and Evans, and is of great interest now, with optimal regularity of solutions yet open. In the metric setting, and indeed even in the weighted Euclidean setting, studies of such solutions are possible under certain conditions on the metric space. One condition is the existence of ∞-harmonic function. In this talk we will discuss this inequality, and a geometric and analytic characterizations of this inequality.