Measuring axial symmetry in convex cones

The problem of measuring the degree of central symmetry of a convex body has been treated by various authors since the early twentieth century. This work addresses the issue of measuring the degree of axial symmetry of a convex cone. Passing from central symmetry in convex bodies to axial symmetry in convex cones is not a mere routine. Although it is possible to push the parallelism between both issues at a great level of generality, there are a number of substantial differences as well. Mathematics Subject Classification: 47L07, 52A20, 52A40, 52A41.