Some regularity results for p-harmonic mappings between Riemannian manifolds. (November 2019) - Guo, Chang-Yu; Xiang, Chang-Lin
Abstract: Let M be a C 2 -smooth Riemannian manifold with boundary and N a complete C 2 -smooth Riemannian manifold. We show that each stationary p -harmonic mapping u : M → N, whose image lies in a compact subset of N, is locally C 1, α for some α ∈ ( 0, 1 ), provided that N is simply connected and has non-positive sectional curvature. We also prove similar results for minimizing p -harmonic mappings with image being contained in a regular geodesic ball. Moreover, when M has non-negative Ricci curvature and N is simply connected with non-positive sectional curvature, we deduce a gradient estimate for C 1 -smooth weakly p -harmonic mappings from which follows a Liouville-type theorem in the same setting.