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SUMMARY:Christine Breiner (Brown University)
DTSTART:20210914T150000Z
DTEND:20210914T160000Z
DTSTAMP:20260423T022721Z
UID:Geolis/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/56/">
 Harmonic branched coverings and uniformization of CAT(k) spheres</a>\nby C
 hristine Breiner (Brown University) as part of Geometria em Lisboa (IST)\n
 \n\nAbstract\nConsider a metric space $(S\,d)$ with an upper curvature bou
 nd in the sense of Alexandrov (i.e.~via triangle comparison). We show that
  if $(S\,d)$ is homeomorphically equivalent to the $2$-sphere\, then it is
  conformally equivalent to the $2$-sphere. The method of proof is through 
 harmonic maps\, and we show that the conformal equivalence is achieved by 
 an almost conformal harmonic map. The proof relies on the analysis of the 
 local behavior of harmonic maps between surfaces\, and the key step is to 
 show that an almost conformal harmonic map from a compact surface onto a s
 urface with an upper curvature bound is a branched covering. This work is 
 joint with Chikako Mese.\n
LOCATION:https://researchseminars.org/talk/Geolis/56/
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