Introduction; On the Minimization of Area Among Chord-Convex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation

4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence of Measurable Sets, 1lep
7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 Ck-Submanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks