The spectral diameter of a symplectic ellipsoid
Habib Alizadeh, Marcelo S. Atallah, Dylan Cant
TL;DR
This paper establishes a precise formula for the spectral diameter of symplectic ellipsoids, improving bounds and exploring its relation to packings, advancing understanding in symplectic geometry.
Contribution
It provides a simple formula for the spectral diameter of symplectic ellipsoids and relates it to packings by two balls, enhancing previous bounds.
Findings
Spectral diameter of a symplectic ball equals its capacity.
The spectral diameter of a symplectic ellipsoid can be explicitly calculated.
Relationship between spectral diameter and packings by two balls is analyzed.
Abstract
The spectral diameter of a symplectic ball is shown to be equal to its capacity; this result upgrades the known bound by a factor of two and yields a simple formula for the spectral diameter of a symplectic ellipsoid. We also study the relationship between the spectral diameter and packings by two balls.
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Taxonomy
TopicsSatellite Image Processing and Photogrammetry · Advanced Numerical Analysis Techniques · Soil, Finite Element Methods