Institute of Mathematics for Industry

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Variational Theory of Surfaces in Four Dimensional Lorentzian Manifolds


Hold Date 2016-06-24 16:00~2016-06-24 17:30

Place Lecture Room M W1-C-513, West Zone 1, Ito campus, Kyushu University

Object person researchers and graduate students 

Speaker Bennett Palmer (Idaho State University, USA)

Abstract:
In this talk we will discuss the variational theory of two dimensional space like surfaces in four dimensional Lorentzian manifolds. Surfaces of zero mean curvature arise as critical points of the area functional, however these surfaces never locally minimize nor locally maximize area. In Lorentz-Minkowski space, a large class of zero mean curvature surfaces locally minimize area when compared with nearby marginally trapped surfaces having the same boundary values to first order. We discuss a convergent flow in the space of marginally trapped surfaces under which a given surface flows, with the boundary values fixed to first order,  to one with zero mean curvature.

We will also discuss the problem of minimizing area among marginally trapped surfaces in Roberton-Walker space times and their relation with variational problems in three dimensional Euclidean space.