A new dual pair of variational problems relates maximum variance of short maps into Hilbert space to maximization of a Bakry-Emery eigenvalue, with explicit solutions on T^2 and SU(2) and an isometric immersion theorem.
Fujiwara, Eigenvalues of Laplacians on a closed Riemannian manifold and its nets, Proc
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First-eigenvalue maximization and inflation of maps
A new dual pair of variational problems relates maximum variance of short maps into Hilbert space to maximization of a Bakry-Emery eigenvalue, with explicit solutions on T^2 and SU(2) and an isometric immersion theorem.