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CATEGORIES:Junior Geometry Seminar
SUMMARY:The Allen-Cahn construction of minimal hypersurfac
es - Fritz Hiesmayr (Cambridge)
DTSTART;TZID=Europe/London:20170428T150000
DTEND;TZID=Europe/London:20170428T160000
UID:TALK71254AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71254
DESCRIPTION:The existence of embedded minimal hypersurfaces is
a question that eluded geometric analysts for the
better part of the twentieth century\; it was eve
ntually settled in 1981 via the so-called Almgren-
Pitts construction. This construction on min-max a
rguments for a suitably enlarged space of hypersur
faces\, and relies on machinery from geometric mea
sure theory.\n\nMy talk will instead focus on a mo
re recent approach to the problem\, where one cons
tructs minimal hypersurfaces that arise from the l
evel sets of solutions to an elliptic PDE\, called
the Allen-Cahn equation. I will present an overvi
ew of this theory that requires no prior knowledge
of geometric analysis.
LOCATION:MR13
CONTACT:
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