Abstract
In 1955 Alexandrov [2, 7, p. 147] introduced the method of planar reflection as a procedure for proving symmetry of closed surfaces of constant mean curvature. In subsequent years, a number of refinements were given, and the method was applied successfully to other problems in differential geometry and partial differential equations, cf. [10, 5, 12, 9, 3, 12]. In the present paper, we introduce a new procedure for obtaining symmetry which may be considered an extension of the planar reflection method to reflection about spheres.
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