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SUMMARY:Min-max\, phase transitions and minimal hypersurfaces. - Marco Gua
 raco (IMPA)
DTSTART:20151127T150000Z
DTEND:20151127T160000Z
UID:TALK62692@talks.cam.ac.uk
CONTACT:Harsha Hutridurga
DESCRIPTION:We present a new min-max method for constructing embedded\nmin
 imal\nhypersurfaces in an arbitrary closed manifold of any dimension. Our\
 napproach is variational\, but it is substantially different from\nAlmgren
 -Pitts theory since it is based on the strong correspondence\nbetween\nthe
  theory of phase transitions and the theory of minimal hypersurfaces.\nAs\
 na preliminary\, we use ideas of Pitts to extend to the case of critical\n
 points of any index\, recent results of Tonegawa-Wickramasekera for stable
 \nphase transitions. We also study the correspondence of critical points\n
 between both theories from a "global" variational point of view in the\nca
 se\nof those obtained by min-max. In particular\, we compare our construct
 ion\nof\na minimal hypersurface with that of Almgren-Pitts and its refinem
 ent by\nSimon-Smith in dimension 3.
LOCATION:CMS\, MR13
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