A special class of isothermic s-embeddings lifts to discrete maximal surfaces in Lorentz space, and the associated family preserves the Ising X-variables.
Bobenko and Tim Hoffmann
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Discrete Lorentz surfaces and s-embeddings II: maximal surfaces
A special class of isothermic s-embeddings lifts to discrete maximal surfaces in Lorentz space, and the associated family preserves the Ising X-variables.