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Bull. Korean Math. Soc. 2023; 60(1): 225-235

Online first article November 7, 2022      Printed January 31, 2023

https://doi.org/10.4134/BKMS.b220059

Copyright © The Korean Mathematical Society.

Bisectors in the Heisenberg group I

Gaoshun Gou, Yueping Jiang, Ioannis D. Platis

Chongqing-University of Posts and Telecommunications; Hunan University; University Campus

Abstract

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We show that metric bisectors with respect to the Kor\'anyi metric in the Heisenberg group are spinal spheres and vice versa. We also calculate explicitly their horizontal mean curvature.

Keywords: Bisector, Heisenberg group, Kor\'anyi metric

MSC numbers: Primary 51M10, 53A10, 53C17, 57M50

Supported by: Part of this work has been carried out while IDP was visiting Hunan University, Changsha, PRC. Hospitality is gratefully appreciated. This work was financially supported by NSFC(No.11631010), NSFC (No.11901061) and cstc2021jcyj-msxmX0647.

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