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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Regularity Theorems for Minimal Two-Valued Graphs.
- Spencer Hughes (Cambridge)
DTSTART;TZID=Europe/London:20140203T150000
DTEND;TZID=Europe/London:20140203T160000
UID:TALK50679AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/50679
DESCRIPTION:The use of multi-valued functions in analysing the
singularities of minimal\nsubmanifolds is well-es
tablished. They were used by Almgren\, for example
\, in\nestimating the size of the singular set of
an area-minimizing current and\nmore recently by W
ickramasekera in work describing the branch points
of\nstable\, minimal hypersurfaces. Despite progr
ess in these contexts\, gaining\nprecise descripti
ons of the singularities of minimal (i.e. `station
ary' \,\nbut not necessarily stable or area-minimi
zing) submanifolds is still\ndifficult and many fu
ndamental questions are open. \n\nIn this talk I w
ill describe some recent results on the regularity
and\nsingularity theory of minimal two-valued Lip
schitz graphs in arbitrary\ncodimension. In codime
nsion one\, there is something like classical elli
ptic\nregularity in that a two-valued Lipschitz fu
nction whose graph is minimal must automatically b
e $C^{1\,\\alpha}$ (as a two-valued function). Nat
urally\,\nin higher codimension things are more co
mplicated and the focus is on\ndescribing the loca
l asymptotic nature of the graph close to singular
\npoints.\n
LOCATION:CMS\, MR13
CONTACT:Prof. Neshan Wickramasekera
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