Skip to content
DraconiticResearch
Search Sources API
179,152 studies31 sourcesUpdated 57 min ago
PreprintCC BY 4.0arXiv

Doubling, Poincaré and Gromov-Hausdorff precompactness for tamed spaces

  • Mathias Braun
  • Chiara Rigoni
  • Christian Rose
  • David Tewodrose
Open at sourcePDFDOICite

Abstract

We establish local volume doubling and a local L2-Poincaré inequality for metric measure spaces tamed by a measure in the extended Kato class that satisfy the bounded interpolation property. To this end, we construct a bi-Lipschitz time change to a metric measure space satisfying a uniform lower Ricci curvature bound. As an application, we obtain pointed measured Gromov-Hausdorff precompactness for such spaces.

Related

  1. Steiner Minimal Trees in the Gromov--Hausdorff Space and in Gromov--Hausdorff Clouds
    I. N. Mikhailov
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds
    Romy Marie Merkel
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. Pointed Gromov-Hausdorff Distance between lp-Wedge Sums and Isometric Embeddings of l∞
    Emin Abdullaev
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Poincaré inequalities, logarithmic growth and doubling
    Joaquim Martin
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  5. An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space
    Takuma Byakuno
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{braun2026doubling,
  title = {{Doubling, Poincaré and Gromov-Hausdorff precompactness for tamed spaces}},
  author = {Mathias Braun and Chiara Rigoni and Christian Rose and David Tewodrose},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11478},
  eprint = {2610.11478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11478},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Doubling, Poincaré and Gromov-Hausdorff precompactness for tamed spaces
AU  - Mathias Braun
AU  - Chiara Rigoni
AU  - Christian Rose
AU  - David Tewodrose
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11478
UR  - https://arxiv.org/abs/2610.11478
AB  - We establish local volume doubling and a local L^2-Poincaré inequality for metric measure spaces tamed by a measure in the extended Kato class that satisfy the bounded interpolation property. To this end, we construct a bi-Lipschitz time change to a metric measure space satisfying a uniform lower Ricci curvature bound. As an application, we obtain pointed measured Gromov-Hausdorff precompactness for such spaces.
ER  -