On the optimal conformal capacity of linked curves

André Guerra; Eden Prywes

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arXiv · 2305.17015

On the optimal conformal capacity of linked curves

André Guerra·Eden Prywes

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Abstract

We investigate the following optimization problem: what is the least possible conformal capacity of a pair of linked curves in $S^3$? A natural conjecture, due to Gehring, Martin and Palka, is that the optimal value is attained by the standard Hopf link. We prove that this is the case under the assumption that each component of the link lies on a different side of a conformal image of the Clifford torus. In particular, this shows that the Hopf link is a local minimizer in a strong sense.

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André Guerra, Eden Prywes. 2023-05-26. On the optimal conformal capacity of linked curves. https://arxiv.org/abs/2305.17015

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