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Volume, surface area and inward injectivity radius
Author(s):
Nobuhiro
Innami
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3049-3055.
MSC (1991):
Primary 53C20;
Secondary 53A07, 53C42, 53C45
Posted:
April 23, 1999
MathSciNet review:
1605968
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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:
- 1.
- A. Gray, Tubes, Reading Mass., Addison-Wesley, 1990. MR 92d:53002
- 2.
- H. Hotelling, Tubes and spheres in
 -spaces, and a class of statistic problems, Amer. J. Math. 61 (1939), 440-460. - 3.
- N. Innami, Isoperimetric inequalities depending on injectivity radius from boundary, Complex Structures And Vector Fields, (Editors S. Dimiev & K. Sekigawa), World Scientific, Singapore, 1995, pp. 36-45. MR 96m:53062
- 4.
- H. Nakagawa, Global Riemannian Geometry, Kaigaishuppanboueki, Tokyo, 1977, (in Japanese).
- 5.
- F. Warner, Foundations of Differentiable Manifolds And Lie Groups, Scott, Foresman and Company, Illinois, 1971. MR 45:4312
- 6.
- 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
Email:
innami@math.sc.niigata-u.ac.jp
DOI:
10.1090/S0002-9939-99-04878-9
PII:
S 0002-9939(99)04878-9
Keywords:
Volume,
surface area,
injectivity radius,
tube
Received by editor(s):
March 6, 1997
Received by editor(s) in revised form:
December 23, 1997
Posted:
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 of article:
Copyright
1999,
American Mathematical Society
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