Almost isoperimetric extremisers of two subriemannian probability measures

Q: What type of study is this?

This is a Quantitative Study study.

Yaozhong W. Qiu

doi:10.48550/arxiv.2509.10889

September 13, 2025Open Access

Almost isoperimetric extremisers of two subriemannian probability measures

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Key Points

Almost isoperimetric extremisers exist in two classes of probability measures, expanding geometric understanding.
Key findings indicate these extremisers can be interpreted as anisotropic half-spaces, a novel concept in geometry.
The research focuses on two distinct spaces: Grushin space and a stratified Lie group, both significant in subriemannian geometry.
Insights gained from this study may have implications for understanding the structure of probability measures in geometric contexts.

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Implication

This research demonstrates the existence of almost isoperimetric extremisers in subriemannian spaces, suggesting new geometric insights.

Abstract

We prove the existence of almost isoperimetric extremisers for two classes of probability measures defined respectively on the Grushin space and a stratified Lie group. It turns out such extremisers can be regarded as a type of anisotropic half-space.

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Cite This Study

Yaozhong W. Qiu (2025) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0929d https://doi.org/10.48550/arxiv.2509.10889

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Almost isoperimetric extremisers of two subriemannian probability measures

Key Points

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Implication

Abstract

Discussion

Cite This Study

Almost isoperimetric extremisers of two subriemannian probability measures

Key Points

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Implication

Abstract

Discussion

Cite This Study

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