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SUMMARY:A canonical foliation for the bubblesheet singularities of geometr
 ic flows - Jean Lagacé (KCL)
DTSTART:20241028T140000Z
DTEND:20241028T150000Z
UID:TALK222904@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:At the core of differential geometry is the notion that the im
 portant features of a space should remain invariant under changes of coord
 inates. Nevertheless\, spaces with special structure may admit preferred c
 oordinate systems\, highlighting some of its features with particular clar
 ity. Such distinguished parameterisations have often been found by identif
 ying a foliation of the space by submanifolds canonically determined by it
 s geometry. An example is foliations by constant mean curvature (CMC) hype
 rsurfaces\, which have been used for instance to parameterise the ends of 
 asymptotically flat manifold\, leading to a definition of\ncenter of mass 
 for isolated gravitating systems. They also played a crucial role in the f
 irst proof of the stability of Minkowski spacetime\, or in foliating geome
 tric "necks" to continue geometric flows through neck singularities via su
 rgery. In the codimension $n \\ge 2$ setting\, the situation is more compl
 icated. Indeed\, where the CMC condition would naturally be replaced by Pa
 rallel Mean Curvature (PMC)\, there are generic geometric obstructions for
  the establishment of such a foliation. In this work\, we introduce a new\
 , pseudodifferential\, curvature condition\, which we dub "Quasi-Parallel 
 Mean Curvature" (QPMC)\, and find that bubblesheet singularities (the high
 er codimension counterpart to necks) can be foliated by QPMC embedded sphe
 res. I will present this curvature condition and the construction of the f
 oliation\, as well as examples that indicate the necessity of such a condi
 tion. Time permitting\, I may present some applications to Mean Curvature 
 Flow.\n\nThis is joint work with Stephen Lynch.
LOCATION:MR13
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