An Isoperimetric-Type Inequality for Spacelike Submanifold in the Minkowski Space

Abstract

We prove an isoperimetric-type inequality for maximal, spacelike submanifold in the Minkowski space. The argument is based on the recent work of Brendle.

Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds

“…where C(Σ) is the region between Σ and a × S and ϕ is the function which gives equality on the coordinate slices. We also mention the work of Tsai-Wang [56] in 2020 which established an isoperimetric-type inequality for maximal, spacelike submanifolds in Minkowski space. With a slightly different perspective, Graf-Sormani in [28] have recently improved on Truede-Grant [55] by establishing upper bounds on the Lorentzian area and volumes of slices of the time-separation function from a Cauchy hypersurface in terms of its mean curvature.…”