Characterising 1-rectifiable metric spaces via connected tangent spaces

Q: What type of study is this?

This is a Quantitative Study study.

David Bate; Phoebe Valentine

doi:10.48550/arxiv.2503.15159

March 19, 2025Open Access

Characterising 1-rectifiable metric spaces via connected tangent spaces

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Key Points

1-rectifiability of a set in complete metric spaces is proved under specific conditions.
The key condition involves the connectedness of all tangent spaces in the metric space.
The set's Hausdorff measure must be finite and lower density positive almost everywhere.
This work enriches the understanding of geometric properties in metric spaces.

Implication

Mathematical proof demonstrates that connected tangent spaces in complete metric spaces imply 1-rectifiability.

Abstract

We prove that in a complete metric space X, $1$-rectifiability of a set E⊂ X with H¹(E)<∞ and positive lower density H¹-a.e. is implied by the property that all tangent spaces are connected metric spaces.

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Cite This Study

Bate et al. (2025) studied this question.

synapsesocial.com/papers/68e62de1a8c0c6d45874006d https://doi.org/10.48550/arxiv.2503.15159

View Full Paper

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Characterising 1-rectifiable metric spaces via connected tangent spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

Characterising 1-rectifiable metric spaces via connected tangent spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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