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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Sufficient conditions for one domain to contain another in a space of constant curvature
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by Jiazu Zhou PDF
Proc. Amer. Math. Soc. 126 (1998), 2797-2803 Request permission

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
  • Received by editor(s): April 25, 1996
  • Received by editor(s) in revised form: February 18, 1997
  • Communicated by: Christopher B. Croke
  • © Copyright 1998 American Mathematical Society
  • 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