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arXiv · 2203.03846

Delaunay decompositions minimizing energy of weighted toroidal graphs

Wai Yeung Lam
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Abstract

Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition.

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Wai Yeung Lam. 2022-03-08. Delaunay decompositions minimizing energy of weighted toroidal graphs. https://arxiv.org/abs/2203.03846

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