Isoperimetric Inequalities in Unbounded Convex Bodies Donal Carbaugh Morris Fairstein

Morris Fairstein

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Isoperimetric Inequalities in Unbounded Convex Bodies Donal Carbaugh Morris FairsteinWe consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C ? Rn, without assuming any further regularity on the boundary of C. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of unbounded convex body with uniform geometry. We then provide a handy characterization of the uniform geometry property and, by exploiting the notion of