Rigid-flexible values for embeddings of four-dimensional ellipsoids into almost-cubes
Year: 2026
Type: article
Abstract: We consider the embedding function c b ( a ) describing the problem of symplectically embedding an ellipsoid E (1, a ) into the smallest possible scaling by λ > 1 of the polydisc P (1, b ). In particular, we calculate rigid-flexible values, i.e. the minimum a such that for E (1, a ′) with a ′ > a , the embedding problem is determined only by the volume. For 1 < b < 2 with b ≠ n + 1 n 2 $b \neq\left(\frac{n+1}{n}\right)^2$ for all n ∈ ℕ, we find that these values vary piecewise smoothly. As Jin and Lee have analyzed the packing stability in the case b > 2, our results complete the story outside of a discrete set.
Source: Advances in Geometry
Authors: Cory H. Colbert, Andrew Lee
Institutions: Washington and Lee University, Adelphi University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7119803126