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SUMMARY:Regularity Theorems for Minimal Two-Valued Graphs. - Spencer Hughe
 s (Cambridge)
DTSTART:20140203T150000Z
DTEND:20140203T160000Z
UID:TALK50679@talks.cam.ac.uk
CONTACT:Prof. Neshan Wickramasekera
DESCRIPTION:The use of multi-valued functions in analysing the singulariti
 es of minimal\nsubmanifolds is well-established. They were used by Almgren
 \, for example\, in\nestimating the size of the singular set of an area-mi
 nimizing current and\nmore recently by Wickramasekera in work describing t
 he branch points of\nstable\, minimal hypersurfaces. Despite progress in t
 hese contexts\, gaining\nprecise descriptions of the singularities of mini
 mal (i.e. `stationary' \,\nbut not necessarily stable or area-minimizing) 
 submanifolds is still\ndifficult and many fundamental questions are open. 
 \n\nIn this talk I will describe some recent results on the regularity and
 \nsingularity theory of minimal two-valued Lipschitz graphs in arbitrary\n
 codimension. In codimension one\, there is something like classical ellipt
 ic\nregularity in that a two-valued Lipschitz function whose graph is mini
 mal must automatically be $C^{1\,\\alpha}$ (as a two-valued function). Nat
 urally\,\nin higher codimension things are more complicated and the focus 
 is on\ndescribing the local asymptotic nature of the graph close to singul
 ar\npoints.\n
LOCATION:CMS\, MR13
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