Acta Mathematica Vietnamica

, Volume 44, Issue 4, pp 915–922 | Cite as

Volume of Sublevel Sets Versus Area of Level Sets via Gelfand-Leray Form

  • Duc Tai TrinhEmail author


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.


Differential form Gelfand-Leray form Sublevel sets Volume and area 

Mathematics Subject Classification (2010)

58A10 26B15 



We would like to thank the referees for their helpful suggestions and comments on the paper.

Funding Information

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2017.324.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DalatDalatVietnam

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