2010/10/20 by Jesse Gell‐Redman, Gell-Redman, Jesse · 1 citation
Mathematics · #35R01 58E20 53C43 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1010.4156
openalex publication_date 2010/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the existence and uniqueness of harmonic maps in degree one homotopy\nclasses of closed, orientable surfaces of positive genus, when the target has\nconic points with cone angles less than 2\π. For a cone point p of cone\nangle less than or equal \π we show that one can minimize, uniquely, in the\nrelative homotopy class of a homeomorphism sending a fixed point q in the\ndomain to p. The latter can be interpreted as minimizing maps from punctured\nRiemann surfaces.\n