Volume, surface area and inward injectivity radius

We show some relations among the volumes of domains in Euclidean spaces, their surface areas and the inward injectivity radii from their boundaries. In particular, we give an estimate for the upper bound of the ratios of their surface areas and volumes by means of inward injectivity radii. The upper...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1999-10, Vol.127 (10), p.3049-3055
Main Author: Innami, Nobuhiro
Format: Article
Language:English
Subjects:
Curvature
Differential topology
Focal points
Hyperspheres
Hypersurfaces
Mathematical functions
Mathematical theorems
Surface areas
Topological theorems
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Summary:We show some relations among the volumes of domains in Euclidean spaces, their surface areas and the inward injectivity radii from their boundaries. In particular, we give an estimate for the upper bound of the ratios of their surface areas and volumes by means of inward injectivity radii. The upper bound seems to depend on their topological structures.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-04878-9