Characterising 1-rectifiable metric spaces via connected tangent spaces

David Bate; Phoebe Valentine

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arXiv · 2503.15159

Characterising 1-rectifiable metric spaces via connected tangent spaces

David Bate·Phoebe Valentine

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Abstract

We prove that in a complete metric space $X$, $1$-rectifiability of a set $E\subset X$ with $\mathcal{H}^1(E)<\infty$ and positive lower density $\mathcal{H}^1$-a.e. is implied by the property that all tangent spaces are connected metric spaces.

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BibTeX RIS

David Bate, Phoebe Valentine. 2026-01-19. Characterising 1-rectifiable metric spaces via connected tangent spaces. https://arxiv.org/abs/2503.15159

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