2017/07/18 by Trinh Duc Tai, Tai, Trinh Duc
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1707.05559
openalex publication_date 2017/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.