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Proceedings of the American Mathematical Society

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

 
 

 

Sufficient conditions for one domain to contain another in a space of constant curvature


Author: Jiazu Zhou
Journal: Proc. Amer. Math. Soc. 126 (1998), 2797-2803
MSC (1991): Primary 52A22, 53C65; Secondary 51M16
DOI: https://doi.org/10.1090/S0002-9939-98-04369-X
MathSciNet review: 1451838
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Abstract: As an application of the analogue of C-S. Chen’s kinematic formula in the 3-dimensional space of constant curvature $\epsilon$, that is, Euclidean space ${\mathbb {R}}^{3}$, $3$-sphere $S^{3}$, hyperbolic space ${\mathbb {H}}^{3}$ ($\epsilon =0, +1, -1$, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space $\mathbb {R}^{3}$, or a $3$-sphere $S^{3}$ or a hyperbolic space $\mathbb {H}^{3}$.


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Additional Information

Jiazu Zhou
Affiliation: Department of Mathematics, Sultan Qaboos University, P.O.Box 36, Al-Khod 123, Sultanate of Oman
Address at time of publication: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015-3174
MR Author ID: 245435
Email: jiz3@lehigh.edu

Keywords: Kinematic formula, transfer principle, Weingarden transformation, Gaussian curvature, convex body, domain, mean curvature, total geodesic curvature.
Received by editor(s): April 25, 1996
Received by editor(s) in revised form: February 18, 1997
Communicated by: Christopher B. Croke
Article copyright: © Copyright 1998 American Mathematical Society