Calculus of Variations and Geometric Measure Theory

P. Tilli

Isoperimetric inequalitites for convex hulls and related questions

created by tilli on 22 Feb 2008


Accepted Paper

Inserted: 22 feb 2008

Journal: Transactions of the American Mathematical Society
Year: 2007



We consider the problem of maximizing the Lebesgue measure of the convex hull of a connected compact set of prescribed one-dimensional Hausdorff measure. In dimension two, we prove that the only solutions are semicircles. In higher dimension, we prove some isoperimetric inequalities for the convex hull of connected sets, we focus on a classical open problem and we discuss a new possible approach.