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SUMMARY:Structure of branch sets of harmonic functions and minimal submani
 folds - Brian Krummel (DPMMS)
DTSTART:20140129T160000Z
DTEND:20140129T170000Z
UID:TALK49463@talks.cam.ac.uk
CONTACT:Parousia Rockstroh
DESCRIPTION:I will discuss some recent results on the structure of the bra
 nch set of multiple-valued solutions to the Laplace equation and minimal s
 urface system.  It is known that the branch set of a multiple-valued solut
 ion on a domain in $\\mathbb{R}^n$ has Hausdorff dimension at most $n-2$. 
  We investigate the fine structure of the branch set\, showing that the br
 anch set is countably $(n-2)$-rectifiable.  Our result follows from the as
 ymptotic behavior of solutions near branch points\, which we establish usi
 ng a modification of the frequency function monotonicity formula due to F.
  J. Almgren and an adaptation to higher-multiplicity of a "blow-up" method
  due to L. Simon that was originally applied to "multiplicity one" classes
  of minimal submanifolds satisfying an integrability hypothesis.
LOCATION:MR14\, Centre for Mathematical Sciences
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