The measure contraction property and rectifiability

We show that a metric measure space $(X,d,\mathfrak{m})$ with finite upper $N$-density that satisfies $\mathsf{MCP}(K,N)$ is $N$-rectifiable. This removes a unique tangent requirement from arXiv:2505.01151.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39083
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

The measure contraction property and rectifiability

Sean Li
arXiv (Cornell University)
Geometric Analysis and Curvature Flows
preprint

The measure contraction property and rectifiability

Sean Li
preprint en

Abstract

We show that a metric measure space $(X,d,\mathfrak{m})$ with finite upper $N$-density that satisfies $\mathsf{MCP}(K,N)$ is $N$-rectifiable. This removes a unique tangent requirement from arXiv:2505.01151.

arXiv (Cornell University)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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The measure contraction property and rectifiability — Sean Li · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS