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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:On short time existence of the network flow. - Fel
ix Schulze (Free University\, Berlin)
DTSTART;TZID=Europe/London:20110321T160000
DTEND;TZID=Europe/London:20110321T170000
UID:TALK29843AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29843
DESCRIPTION:I will report on joint work with T. Ilmanen and A.
Neves on how to\nprove the existence of an embedd
ed\,\nregular network moving by curve shortening f
low in the plane\, starting from\na non-regular in
itial network.\nHere a regular network consists of
smooth\, embedded line-segments such that\nat eac
h endpoint\, if not infinity\,\nthere are three ar
cs meeting under a 120 degree angle. In the non-re
gular\ncase we allow that an arbitrary number\nof
line segments meet at an endpoint\, without an ang
le condition.\nThe proof relies on gluing in appro
priately scaled self-similarly expanding\nsolution
s and a new monotonicity formula\,\ntogether with
a local regularity result for such evolving networ
ks.\nThis short time existence result also has app
lications in extending such a\nflow of networks th
rough singularities.\n\n
LOCATION:CMS\, MR15
CONTACT:Prof. Neshan Wickramasekera
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