RIESZ ENERGIES AND THE MAGNITUDE OF MANIFOLDS
Gimperlein, Heiko and Goffeng, Magnus LU
(2025)
In Proceedings of the American Mathematical Society
153(7).
p.3173-3184
- Abstract
We study the geometric significance of Leinster’s magnitude invariant. For closed manifolds we find a precise relation with Brylinski’s beta function and therefore with classical invariants of knots and submanifolds. In the special case of compact homogeneous spaces we obtain an elementary proof that the residues of the beta function contain the same geometric information as the asymptotic expansion of the magnitude function. For general closed manifolds we use the recent pseudodifferential analysis of the magnitude operator to relate these via an interpolating polynomial family. Beyond manifolds, the relation with the Brylinski beta function allows to deduce unexpected properties of the magnitude function for the p-adic integers.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f8574ffe-cae4-4df0-856f-661327bede19
- author
- Gimperlein, Heiko
and Goffeng, Magnus
LU
- organization
- publishing date
- 2025-07
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Proceedings of the American Mathematical Society
- volume
- 153
- issue
- 7
- pages
- 12 pages
- publisher
- American Mathematical Society (AMS)
- external identifiers
-
- scopus:105006481868
- ISSN
- 0002-9939
- DOI
- 10.1090/proc/17203
- language
- English
- LU publication?
- yes
- id
- f8574ffe-cae4-4df0-856f-661327bede19
- date added to LUP
- 2025-07-16 13:30:20
- date last changed
- 2025-07-16 13:31:35
@article{f8574ffe-cae4-4df0-856f-661327bede19,
abstract = {{<p>We study the geometric significance of Leinster’s magnitude invariant. For closed manifolds we find a precise relation with Brylinski’s beta function and therefore with classical invariants of knots and submanifolds. In the special case of compact homogeneous spaces we obtain an elementary proof that the residues of the beta function contain the same geometric information as the asymptotic expansion of the magnitude function. For general closed manifolds we use the recent pseudodifferential analysis of the magnitude operator to relate these via an interpolating polynomial family. Beyond manifolds, the relation with the Brylinski beta function allows to deduce unexpected properties of the magnitude function for the p-adic integers.</p>}},
author = {{Gimperlein, Heiko and Goffeng, Magnus}},
issn = {{0002-9939}},
language = {{eng}},
number = {{7}},
pages = {{3173--3184}},
publisher = {{American Mathematical Society (AMS)}},
series = {{Proceedings of the American Mathematical Society}},
title = {{RIESZ ENERGIES AND THE MAGNITUDE OF MANIFOLDS}},
url = {{http://dx.doi.org/10.1090/proc/17203}},
doi = {{10.1090/proc/17203}},
volume = {{153}},
year = {{2025}},
}