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Variational Theory of Surfaces in Four Dimensional Lorentzian Manifolds


開催時期 2016-06-24 16:00~2016-06-24 17:30

場所 九州大学 伊都キャンパス ウエスト1号館 中講義室 W1-C-513

受講対象 研究者・大学院生 

講師 Bennett Palmer (Idaho State University, USA)

【講演要旨】:
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.