A remark on projections of the rotated cube to complex lines
Efim D. Gluskin, Yaron Ostrover
TL;DR
This paper investigates the expected minimal projection area of a randomly rotated cube onto complex lines, motivated by its connection to the cylindrical symplectic capacity, a key symplectic invariant.
Contribution
It introduces a novel analysis linking cube projections to symplectic invariants, providing new insights into geometric properties related to symplectic capacities.
Findings
Derived the expected minimal projection area for a rotated cube onto complex lines
Established connections between geometric projections and symplectic invariants
Provided formulas or bounds related to cylindrical symplectic capacity
Abstract
Motivated by relations with a symplectic invariant known as the "cylindrical symplectic capacity", in this note we study the expectation of the area of a minimal projection to a complex line for a randomly rotated cube.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Advanced Algebra and Geometry