CMC hierarchy
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.
Cite
@article{arxiv.1312.7169,
title = {CMC hierarchy},
author = {Joe S. Wang},
journal= {arXiv preprint arXiv:1312.7169},
year = {2014}
}
Comments
An expanded version of this paper will be posted as a series CMC hierarchy I, II