We can assume that immersed surface divides the space into finite number of regions. Then your formula gives volume of of these regions counted with muliplicity.
Subdivide your surface into singular surfaces such that each cuts only one region. Summing up the isoperimetric inequalities for some of these surfaces implies the inequality that you are looking for.
We can assume that immersed surface divides the space into finite number of regions. Then your formula gives volume of of these regions counted with muliplicity.
Subdivide your surface into singular surfaces such that each cuts only one region. Summing up the isoperimetric inequalities for these surfaces implies the inequality that you are looking for.
We can assume that immersed surface divides the space into finite number of regions. Then your formula gives volume of of these regions counted with muliplicity.
Subdivide your surface into singular surfaces such that each cuts only one region. Summing up the isoperimetric inequalities for some of these surfaces implies the inequality that you are looking for.
