2022/10/21 by Heimendahl, Arne, Lücke, Moritz, Vallentin, Frank +1 · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2210.11952
We derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori ℝn/L, where L is an n-dimensional lattice, into Hilbert spaces. This enables us to provide a constant factor improvement over the previously best lower bound on the minimal distortion of an embedding of an n-dimensional flat torus. As further applications we prove that every n-dimensional flat torus has a finite dimensional least distortion embedding, that the standard embedding of the standard tours is optimal, and we determine least distortion embeddings of all 2-dimensional flat tori.