The principle of symmetry–extremity

摘要

There are several examples which show us a certain relationship between the notion of symmetry and extremity that is when some “object” has a higher symmetry certain quantity (concerning a given property of the object) takes extreme value. It is enough to think about the well-known isoperimetric problem. So by above mentioned quantity we mean a measure defined on some σ-ring. In this paper we would like to study that relationship.