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SUMMARY:Panagiota Daskalopoulos (Columbia)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
DTSTAMP:20260423T005729Z
UID:BOWL/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BOWL/32/">Ty
 pe II smoothing in Mean curvature flow</a>\nby Panagiota Daskalopoulos (Co
 lumbia) as part of B.O.W.L Geometry Seminar\n\n\nAbstract\nIn 1994 Velázq
 uez constructed a smooth $O(4)\\times O(4)$ invariant Mean Curvature Flow 
 that forms a type-II singularity at the origin in space-time.  Recently\, 
 Stolarski showed that the mean curvature on this solution is uniformly bou
 nded.  Earlier\, Velázquez also provided formal asymptotic expansions for
  a possible smooth continuation of the solution after the singularity. \n 
 \nJointly with S. Angenent and N. Sesum we establish the short time existe
 nce of Velázquez' formal continuation\, and we verify that the mean curva
 ture is also uniformly bounded on the continuation. Combined with the earl
 ier results of Velázquez–Stolarski we therefore show that there exists 
 a solution $\\left\\{ M_t^7\\subset \\mathbb{R}^8 | -t_0 < t < t_0\\right\
 \}$ that has an isolated singularity at the origin $0$ in $\\mathbb{R}^8$\
 , and at $t=0$\; moreover\, the mean curvature is uniformly bounded on thi
 s solution\, even though the second fundamental form is unbounded near the
  singularity.\n
LOCATION:https://researchseminars.org/talk/BOWL/32/
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