Acta Mathematica Vietnamica

, Volume 44, Issue 4, pp 915–922

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

• Duc Tai Trinh
Article

## Abstract

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.

## Keywords

Differential form Gelfand-Leray form Sublevel sets Volume and area

58A10 26B15

## Notes

### Acknowledgements

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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