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arXiv · 2402.16223

Rigid-flexible values for symplectic embeddings of four-dimensional ellipsoids into almost-cubes

Andrew Lee·Cory H. Colbert
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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 $\lambda>1$ 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 volume. For $1 2$, our results complete the story outside of a discrete set.

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Andrew Lee, Cory H. Colbert. 2024-02-25. Rigid-flexible values for symplectic embeddings of four-dimensional ellipsoids into almost-cubes. https://arxiv.org/abs/2402.16223

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