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.