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Non-Hilbertian tangents to Hilbertian spaces

Part of: Linear function spaces and their duals Global differential geometry

Published online by Cambridge University Press:  05 April 2022

Danka Lučić Open the ORCID record for Danka Lučić [Opens in a new window] ,
Enrico Pasqualetto Open the ORCID record for Enrico Pasqualetto [Opens in a new window]  and
Tapio Rajala Open the ORCID record for Tapio Rajala [Opens in a new window]
Danka Lučić
Affiliation:
Università di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy (danka.lucic@dm.unipi.it)
Enrico Pasqualetto
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy (enrico.pasqualetto@sns.it)
Tapio Rajala
Affiliation:
University of Jyvaskyla, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyvaskyla, Finland (tapio.m.rajala@jyu.fi)
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Abstract

We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.

Keywords

Tangent coneInfinitesimal HilbertianityPI space

MSC classification

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 3 , June 2023 , pp. 811 - 832
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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