Existence and uniqueness of harmonic maps from the Sierpinski gasket (and other p.c.f. fractals) to the circle is established for each homotopy class via per-class covering spaces, lifting, harmonic extension, and projection, extending Strichartz's theorem.
Strichartz, Harmonic mappings of the Sierpinski gasket to the circle, Proc
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Kuramoto model on Sierpinski Gasket I: Harmonic maps
Existence and uniqueness of harmonic maps from the Sierpinski gasket (and other p.c.f. fractals) to the circle is established for each homotopy class via per-class covering spaces, lifting, harmonic extension, and projection, extending Strichartz's theorem.