Videos

Constraint equations on compact manifolds with boundary

Presenter
November 20, 2013
Keywords:
  • conformal field theory
  • conformal geometry
  • mean curvature
  • Lichnerowicz equation
  • Lorentzian geometry
MSC:
  • 83Cxx
  • 83-xx
  • 83Fxx
  • 83C30
  • 83C40
  • 83C50
  • 83C60
Abstract
In this talk I will present old and new results on the construction of solutions to the constraint equations with non-constant mean curvature. From previous work with Mattias Dahl and Emmanuel Humbert, it is known that, on closed manifolds, solutions to the conformal constraint equations exist provided that a certain limit equation admits no non-trivial solution. We extend this result to manifolds with boundary with apparent horizon boundary condition.
Supplementary Materials