Curvature exponent and geodesic dimension on Sard-regular Carnot groups
Abstract
In this study, we characterize the geodesic dimension NGEO and give a new lower bound to the curvature exponent NCE on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which NCE GE > N O; this answers a question posed by Rizzi (Measure contraction properties of Carnot groups. Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 60, 20).
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
De Gruyter
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202408165534Use this for linking
Review status
Peer reviewed
ISSN
2299-3274
DOI
https://doi.org/10.1515/agms-2024-0004
Language
English
Published in
Analysis and Geometry in Metric Spaces
Citation
- Nicolussi Golo, S., & Zhang, Y. (2024). Curvature exponent and geodesic dimension on Sard-regular Carnot groups. Analysis and Geometry in Metric Spaces, 12(1), Article 20240004. https://doi.org/10.1515/agms-2024-0004
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Funder(s)
Research Council of Finland
Research Council of Finland
Funding program(s)
Academy Project, AoF
Research costs of Academy Research Fellow, AoF
Akatemiahanke, SA
Akatemiatutkijan tutkimuskulut, SA
Additional information about funding
S.N.G. has been supported by the Academy of Finland (Grant 328846, “Singular integrals, harmonic functions, and boundary regularity in Heisenberg groups,” Grant 322898 “Sub-Riemannian Geometry via Metric-geometry and Lie-group Theory,” Grant 314172 “Quantitative rectifiability in Euclidean and non-Euclidean spaces”).
Copyright© 2024 the Authors