A geometric inequality on a compact domain in $\mathbb R^{n}$
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 1-8
Published online January 31, 2018
Young Do Chai, Yong Seung Cho
Sungkyunkwan University, Ewha Womans University
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.
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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