Rigid-flexible values for embeddings of four-dimensional ellipsoids into almost-cubes
Abstract
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Point processes and geometric inequalities
Geometric and Algebraic Topology
Publication details
- Journal / source
- Advances in Geometry
- Volume
- 26
- Issue
- 1
- Pages
- 73–93
- Publication date
- 1 January 2026
- Language
- EN