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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Volume, surface area and inward injectivity radius
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by Nobuhiro Innami PDF
Proc. Amer. Math. Soc. 127 (1999), 3049-3055 Request permission

Abstract:

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.
References
  • Alfred Gray, Tubes, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1990. MR 1044996
  • H. Hotelling, Tubes and spheres in $n$-spaces, and a class of statistic problems, Amer. J. Math. 61 (1939), 440–460.
  • Nobuhiro Innami, Isoperimetric inequalities depending on injectivity radius from boundary, Complex structures and vector fields (Pravetz, 1994) World Sci. Publ., River Edge, NJ, 1995, pp. 36–45. MR 1376145
  • H. Nakagawa, Global Riemannian Geometry, Kaigaishuppanboueki, Tokyo, 1977, (in Japanese).
  • Frank W. Warner, Foundations of differentiable manifolds and Lie groups, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0295244
  • H. Weyl, On the volume of tubes, Amer. J. Math. 61 (1939), 461–472.
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Additional Information
  • Nobuhiro Innami
  • Affiliation: Department of Mathematics and Information, Graduate School of Science and Technology, Niigata University, Niigata, 950-2181, Japan
  • MR Author ID: 199776
  • Email: innami@math.sc.niigata-u.ac.jp
  • Received by editor(s): March 6, 1997
  • Received by editor(s) in revised form: December 23, 1997
  • Published electronically: April 23, 1999
  • Additional Notes: The author was partly supported by the Grants-in-Aid for Scientific Research, the Ministry of Education, Science and Culture, Japan.
  • Communicated by: Christopher Croke
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3049-3055
  • MSC (1991): Primary 53C20; Secondary 53A07, 53C42, 53C45
  • DOI: https://doi.org/10.1090/S0002-9939-99-04878-9
  • MathSciNet review: 1605968