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SUMMARY:Regularity Theory of Energy Minimising Maps - Paul	Minter
DTSTART:20180315T143000Z
DTEND:20180315T153000Z
UID:TALK103033@talks.cam.ac.uk
CONTACT:Kasia Wyczesany
DESCRIPTION:For C^1^ maps between Riemannian manifolds\, we can define the
 ir Dirichlet energy. When the target manifold is R^m^ with the Euclidean m
 etric\, critical points of the Dirichlet energy are harmonic\, and so thei
 r regularity is easy to establish. However in general this is not the case
  as the curvature causes the Euler-Lagrange equations to become non-linear
 . In this case\, the regularity theory is more subtle\, and the possibilit
 y of a small singular set arises. In this talk I will discuss both cases\,
  working up to the statement of the Schoen-Uhlenbeck theorem\, which is th
 e main result for establishing the regularity theory of such maps. We will
  then discuss the size of the singular set which can arise.
LOCATION:MR11
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