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.
S ´aenz, Introduction to harmonic analysis, Student Mathematical Library, vol
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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.