Volume of Sublevel Sets Versus Area of Level Sets via Gelfand-Leray Form
Duc Tai Trinh
In this paper, we give a relation between the volume of sublevel sets and the area of level sets using a Gelfand-Leray form. As a consequence, we give an estimation of the volume of sublevel sets. In particular, we give a proof of the known fact that the derivative of the volume of a $n$-dimensional ball with respect to the radius equals the area of the sphere which bounds the $n$-dimensional ball.