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SUMMARY:Tangent Cones and Minimal Hypersurface Singularities - Paul Minter
  (University of Cambridge)
DTSTART:20191115T160000Z
DTEND:20191115T170000Z
UID:TALK131386@talks.cam.ac.uk
CONTACT:Nils Prigge
DESCRIPTION:Critical points of the area functional are known as minimal su
 rfaces\, and in the case of graphs over domains in Euclidean space they sa
 tisfy the so-called minimal surface equation. In high dimensions it is pos
 sible for area minimising surfaces to be singular\, as illustrated by Simo
 ns cone. In this talk we will discuss several results surrounding the sing
 ular set of minimal hypersurfaces\, including Allard's regularity theorem 
 and dimension bounds. To establish bounds on the dimension of the singular
  set we will study the possible tangent cones to the hypersurface\, which 
 are formed by taking weak limits when "blowing up" the hypersurface at a g
 iven point. This is done by establishing monotonicity formulae\, compactne
 ss results\, and the non-existence of certain cones in low dimensions. Tim
 e permitting\, we will mention how such techniques can be used to prove th
 e Bernstein theorem\, which tells us that entire minimal graphs in dimensi
 ons less than 8 are in fact planar.
LOCATION:MR13
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