The Euclidean isoperimetric problem
In this chapter we study the Euclidean isoperimetric problem,
characterizing its minimizers as the Euclidean balls of measure m. Taking into account that P(B) = n, this result will be equivalent to proving the following Euclidean isoperimetric inequality.
Theorem 14.1 If E is a Lebesgue measurable set in with |E| < , then
Equality holds if and only if |EB(x, r)| = 0 for some x , r > 0.
Remark 14.2 When ...