H\"{o}lder continuity of energy minimizer maps between riemannian polyhedra

Abstract

The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the h\"{o}lder continuity of local energy minimizers between Riemannian polyhedra with the target spaces without focal points. With this new result, we also complete our existence theorem obtained in [5], and consequently we generalize completely, to the case of target polyhedra without focal points (which is weaker geometric condition than the nonpositivity of the curvature), the Eells-fuglede's existence and regularity theorem [12, chapters 10, 11] which is the new version of the famous Eells-Sampson's theorem [13].