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The global structure of constant mean curvature surfaces. (English) Zbl 0803.53040

Let MC1 denote a complete, finite topology, properly embedded surface with constant mean curvature 1. Kapouleas constructed a wealth of MC1 surfaces by starting with a linear graph in \(\mathbb{R}^ 3\) satisfying a balancing condition at each vertex. The present authors prove global properties of MC1 surfaces giving partial answers to a conjecture that all MC1 surfaces “look like Kapouleas examples” in some sense. In particular they use a force and torque vector assigned invariantly to each homology class of 1-cycles on an MC1 surface.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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References:

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