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Bull. Korean Math. Soc. 2018; 55(1): 1-8
Online first article December 21, 2017 Printed January 31, 2018
https://doi.org/10.4134/BKMS.b160093
Copyright © The Korean Mathematical Society.
A geometric inequality on a compact domain in $\mathbb R^{n}$
Young Do Chai, Yong Seung Cho
Sungkyunkwan University, Ewha Womans University
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.
Keywords: $C(o)$-compact domain, Morse theory, Euler characteristic, focal point, cell complex, homology sequence, integral of mean curvature
MSC numbers: 53C23, 49Q20
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