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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Structure of branch sets of harmonic functions and
minimal submanifolds - Brian Krummel (DPMMS)
DTSTART;TZID=Europe/London:20140129T160000
DTEND;TZID=Europe/London:20140129T170000
UID:TALK49463AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49463
DESCRIPTION:I will discuss some recent results on the structur
e of the branch set of multiple-valued solutions t
o the Laplace equation and minimal surface system.
It is known that the branch set of a multiple-va
lued solution on a domain in $\\mathbb{R}^n$ has H
ausdorff dimension at most $n-2$. We investigate
the fine structure of the branch set\, showing tha
t the branch set is countably $(n-2)$-rectifiable.
Our result follows from the asymptotic behavior
of solutions near branch points\, which we establi
sh using a modification of the frequency function
monotonicity formula due to F. J. Almgren and an a
daptation to higher-multiplicity of a "blow-up" me
thod due to L. Simon that was originally applied t
o "multiplicity one" classes of minimal submanifol
ds satisfying an integrability hypothesis.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Parousia Rockstroh
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