A semidefinite program for least distortion embeddings of flat tori into Hilbert spaces

Mathematical Programming 2026 Open access

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Authors: Arne Heimendahl, Moritz Lücke, Frank Vallentin, Marc Christian Zimmermann
DOI: 10.1007/s10107-026-02369-7
Cited by: 0
References: 28

Abstract

Abstract We derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori $$\mathbb {R}^n/L$$ R n / 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 torus is optimal, and we determine least distortion embeddings of all 2-dimensional flat tori.

Fields of Study & Subjects

Cell Adhesion Molecules Research Ferroelectric and Negative Capacitance Devices Advancements in Photolithography Techniques

Publication details

Journal / source
Mathematical Programming
Publisher
Springer Science and Business Media LLC
Volume
218
Issue
1-2
Pages
477–504
Publication date
26 May 2026
Language
EN