October 13, 2025Open Access

On the almost sure spiraling of geodesics in CAT(0) spaces

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A logarithm law-type result reveals the spiraling behavior of geodesics in specific compact subsets.
The study focuses on quotients of rank one CAT(0) spaces and analyzes their geometric structure.
Geodesics are found to spiral around quotients of periodic Morse flats within the context of the research.
The findings enhance the understanding of geometric properties in certain mathematical spaces.

Implication

This study proves a logarithm law for geodesics spiraling around compact subsets in CAT(0) spaces, indicating notable geometric behavior.

Abstract

We prove a logarithm law-type result for the spiraling of geodesics around certain types of compact subsets (e.g. quotients of periodic Morse flats) in quotients of rank one CAT(0) spaces.

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Cite This Study

Bray et al. (2025) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec092e4 https://doi.org/10.48550/arxiv.2509.10944

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Implication

This study proves a logarithm law for geodesics spiraling around compact subsets in CAT(0) spaces, indicating notable geometric behavior.

Abstract

We prove a logarithm law-type result for the spiraling of geodesics around certain types of compact subsets (e.g. quotients of periodic Morse flats) in quotients of rank one CAT(0) spaces.

On the almost sure spiraling of geodesics in CAT(0) spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

On the almost sure spiraling of geodesics in CAT(0) spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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