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arXiv · 1807.11653

The modulus of the Kor\'anyi ellipsoidal ring

Gaoshun Gou·I. D. Platis
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Abstract

The Kor\'anyi ellipsoidal ring $\mathcal{E}$ of radii $B$ and $A$, $0<B<A$, is defined as the image of the Kor\'anyi spherical ring of the same radii and centred at the origin via a linear contact map $L$ in the Heisenberg group. If $K\ge 1$ is the maximal distortion of $L$ then we prove that the modulus of $\mathcal{E}$ is equal to $$ {\rm mod}(\mathcal{E})=\left(\frac{3}{8}\Big(K^2+\frac{1}{K^2}\Big)+\frac{1}{4}\right)\frac{\pi^2}{(\log (A/B))^3}. $$

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Gaoshun Gou, I. D. Platis. 2018-07-31. The modulus of the Kor\'anyi ellipsoidal ring. https://doi.org/10.1090/proc/14434

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