Harmonic branched coverings and uniformization of CAT(<i>k</i>) spheres
Harmonic branched coverings and uniformization of CAT(<i>k</i>) spheres
Abstract Let S be a surface with a metric d satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>S</m:mi> <m:mo>,</m:mo> <m:mi>d</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(S,d)} is …