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

摘要

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 R-3, 3-sphere S-3, hyperbolic space H-3 (epsilon = 0, +1, -1, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space R-3, or a 3-sphere S-3 or a hyperbolic space H-3. [References: 19]