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SUMMARY:On short time existence of the network flow. - Felix Schulze (Free
  University\, Berlin)
DTSTART:20110321T160000Z
DTEND:20110321T170000Z
UID:TALK29843@talks.cam.ac.uk
CONTACT:Prof. Neshan Wickramasekera
DESCRIPTION:I will report on joint work with T. Ilmanen and A. Neves on ho
 w to\nprove the existence of an embedded\,\nregular network moving by curv
 e shortening flow in the plane\, starting from\na non-regular initial netw
 ork.\nHere a regular network consists of smooth\, embedded line-segments s
 uch that\nat each endpoint\, if not infinity\,\nthere are three arcs meeti
 ng under a 120 degree angle. In the non-regular\ncase we allow that an arb
 itrary number\nof line segments meet at an endpoint\, without an angle con
 dition.\nThe proof relies on gluing in appropriately scaled self-similarly
  expanding\nsolutions and a new monotonicity formula\,\ntogether with a lo
 cal regularity result for such evolving networks.\nThis short time existen
 ce result also has applications in extending such a\nflow of networks thro
 ugh singularities.\n\n
LOCATION:CMS\, MR15
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