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SUMMARY:The regularity and existence of branched minimal submanifolds - Br
 ian Krummel (DPMMS)
DTSTART:20120116T160000Z
DTEND:20120116T170000Z
UID:TALK34904@talks.cam.ac.uk
CONTACT:Jonathan Ben-Artzi
DESCRIPTION:Multivalued functions arise naturally in the study of the bran
 ch set of branched minimal immersions. Simon and Wickramasekera (2007) sho
 wed how to construct a large class of multivalued solutions in C^1\,μ^ to
  the Dirichlet problem for the minimal surface equation provided the bound
 ary data satisfied a k-fold symmetry condition. I will show that the branc
 h sets of the minimal hypersurfaces they constructed are real analytic sub
 manifolds\, which involves proving a general regularity result for multiva
 lued solutions to elliptic equations. I also extend their existence result
 \, which was specific to the minimal surface equation\, to show that there
  exists multivalued solutions in C^1\,μ^ to other elliptic equations and 
 to elliptic systems that preserve the k-fold symmetry condition.
LOCATION:CMS\, MR14
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