2016/05/26 by Brian Freidin, Freidin, Brian · 1 citation
Mathematics · Medicine · #53 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Pelvic and Acetabular Injuries
paper · pdf · doi:10.48550/arxiv.1605.08461
openalex publication_date 2016/05/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study harmonic maps from Riemannian manifolds into arbitrary\nnon-positively curved and CAT(-1) metric spaces. First we discuss the domain\nvariation formula with special emphasis on the error terms. Expanding higher\norder terms of this and other formulas in terms of curvature, we prove an\nanalogue of the Eels-Sampson Bochner formula in this more general setting. In\nparticular, we show that harmonic maps from spaces of non-negative Ricci\ncurvature into non-positively curved spaces have subharmonic energy density.\nWhen the domain is compact the energy density is constant, and if the domain\nhas a point of positive Ricci curvature every harmonic map into an NPC space\nmust be constant.\n