Gian Paolo Leonardi, Manuel Ritore, Efstratios Vernadakis
We 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 asymptotic cylinder of C, we prove existence of isoperimetric regions in a generalized sense. By an approximation argument we show the strict...
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C ? Rn, without assuming any furthe...
