ABSTRACT: We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, where the target has conic points with cone angles less than $2pi$. We show that such maps are homeomorphisms. For a cone point $p$ of cone angle less than $pi$ we show that one can minimize with respect to the condition that a fixed point $q$ in the domain maps to $p$.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification