• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.519-529
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• 1995

Let M be a compact smooth manifold of dimension n and let E be a flat (complet) vector bundle over M of rank r.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-8
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• 2018

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.