# A GEOMETRIC INEQUALITY ON A COMPACT DOMAIN IN ℝn

• Chai, Young Do (Department of Mathematics College of Natural Sciences Sungkyunkwan University) ;
• Cho, Yong Seung (Division of Mathematical and Physical Science College of Natural Sciences Ewha Womans University)
• Accepted : 2017.08.10
• Published : 2018.01.31

#### Abstract

In this paper, we study some topological structure of a compact domain in ${\mathbb{R}}^n$ in terms of the curvature conditions and develop a geometric inequality involving the volume and the integral of mean curvatures over the boundary of the compact domain.

#### Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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