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arXiv · 1312.7169

CMC hierarchy

Joe S. Wang
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Abstract

We propose an extension of the differential system for constant mean curvature (CMC) surfaces in a three dimensional space form to an associated hierarchy of evolution equations by the higher-order commuting symmetries. The infinite sequence of higher-order conservation laws of CMC surfaces admit the corresponding extension to the conservation laws of the entire hierarchy. A class of generalized CMC surfaces are introduced as the phase space of the hierarchy. Via a canonical dressing transformation, we define a wave function for CMC hierarchy. This leads to a pair of additional non-local formal Killing fields and the associated spectral (Virasoro) Killing field.

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Joe S. Wang. 2013-12-27. CMC hierarchy. https://arxiv.org/abs/1312.7169

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