Hearing the platycosms
J. P. Rossetti & J. H. Conway
TL;DR
This paper proves the uniqueness of an isospectral pair of compact platycosms, flat Riemannian 3-manifolds without boundary, up to scale, contributing to the spectral geometry understanding.
Contribution
It establishes the first known unique isospectral pair of compact flat 3-manifolds, advancing spectral geometry knowledge.
Findings
Identified a unique isospectral pair of platycosms
Proved the pair's uniqueness up to scale
Contributed to understanding spectral properties of flat manifolds
Abstract
A `platycosm' is a flat Riemannian 3-manifold without boundary. In this paper we prove that there is (up to scale) a unique isospectral pair of compact platycosms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Point processes and geometric inequalities