What does this research mean for the field?

The heights of point orbits of thin subgroups of Bianchi groups exhibit asymptotic local-global behavior. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to establish a connection between local and global properties of heights associated with point orbits of specific groups.

March 10, 2026Open Access

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An asymptotic local–global theorem on heights of some Kleinian group orbits

XXXuanxuan XiaoMacau University of Science and Technology XZXin ZhangChinese University of Hong Kong

Key Points

The aim is to establish a connection between local and global properties of heights associated with point orbits of specific groups.
Proved an asymptotic local-global theorem
Analyzed the heights of point orbits
Focused on thin subgroups of Bianchi groups
Demonstrated significant relationships between local heights and global properties
Contributed to the understanding of the structure of Kleinian groups

Abstract

Abstract We prove an asymptotic local–global theorem on the heights of point orbits of thin subgroups of Bianchi groups in .

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An asymptotic local–global theorem on heights of some Kleinian group orbits

Key Points

Abstract

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