BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Geometric Analysis Seminar
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260711T181207Z
UID:tag:localist.com\,2008:EventInstance_3542904
DTSTART:20180509T200000Z
DTEND:20180509T220000Z
DESCRIPTION:Christos Mantoulidis (MIT)\n\nTitle: “Minimal surfaces and th
 e Allen-Cahn equation on 3-manifolds”\n\nAbstract: This is joint work wi
 th O. Chodosh. The Allen-Cahn equation is a semilinear PDE which is deeply
  linked to the theory of minimal hypersurfaces via a singular limit. Using
  new curvature estimates and sharp sheet separation estimates for stable A
 llen-Cahn solutions on 3-manifolds\, derived by improving recent work of W
 ang-Wei\, we show: minimal surfaces arising from Allen-Cahn solutions with
  bounded energy and bounded Morse index are two-sided and occur with multi
 plicity one and the expected Morse index\, provided the ambient metric is 
 generic. This confirms\, in the Allen-Cahn setting\, two conjectures of Ma
 rques-Neves: a strengthened multiplicity one conjecture\, and the index lo
 wer bound conjecture. If combined with recent work of Guaraco and Gaspar-G
 uaraco\, this gives a new proof of Yau's conjecture on infinitely many min
 imal surfaces in a 3-manifold with a generic metric (recently proven in di
 mensions up to 7 by Irie-Marques-Neves and later Gaspar-Guaraco) with new 
 geometric conclusions.
LOCATION:2-131
SUMMARY:Geometric Analysis Seminar
URL;VALUE=URI:https://calendar.mit.edu/event/geometric_analysis_seminar_854
 4
CATEGORIES:Conferences/Seminars/Lectures
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