A metric space with line-splitting tangents at every point has Hilbert Sobolev spaces for every measure.
Hilbert space factor of metric spaces
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abstract
We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.
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math.MG 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian
A metric space with line-splitting tangents at every point has Hilbert Sobolev spaces for every measure.