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

Zhou, Jiazu

doi:10.1090/S0002-9939-98-04369-X

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