PreprintCC BY 4.0arXiv
Infinitesimal Hilbertianity for manifolds with Sobolev regular Riemannian metrics through uniform lower capacity bounds
Abstract
We prove that metric measure spaces arising from $2$-manifolds equipped with Riemannian metrics g such that g, g−1 ∈ L∞loc ∩ W1,ploc are infinitesimally Hilbertian. Along the way, we establish uniform lower $1$-capacity bounds of several $1$-dimensional subsets of R2.
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BibTeX
@misc{ryborz2026infinitesimal,
title = {{Infinitesimal Hilbertianity for manifolds with Sobolev regular Riemannian metrics through uniform lower capacity bounds}},
author = {Vanessa Ryborz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03373},
eprint = {2610.03373},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03373},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Infinitesimal Hilbertianity for manifolds with Sobolev regular Riemannian metrics through uniform lower capacity bounds
AU - Vanessa Ryborz
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03373
UR - https://arxiv.org/abs/2610.03373
AB - We prove that metric measure spaces arising from $2$-manifolds equipped with Riemannian metrics g such that g, g^−1 ∈ L^∞_loc ∩ W^1,p_loc are infinitesimally Hilbertian. Along the way, we establish uniform lower $1$-capacity bounds of several $1$-dimensional subsets of R^2.
ER -