The relative isoperimetric inequality outside convex domains in R n

Abstract

We prove that the area of a hypersurface which traps a given volume outside a convex domain C in Euclidean space R n is bigger than or equal to the area of a hemisphere which traps the same volume on one side of a hyperplane. Further, when C has smooth boundary ∂C, we show that equality holds if and only if is a hemisphere which meets ∂C orthogonally.

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