Q-valued harmonic functions are functions that minimize the Dirichlet energy and take on values in a finite set of q distinct points. These functions are essential in the study of variational problems, particularly in understanding how they behave in relation to minimizers of Dirichlet energy, which is a measure of how 'smooth' or 'harmonic' a function is over a domain. The interplay between these functions and their associated energies provides deep insights into the geometric and analytic properties of spaces.
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