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THE WILLMORE ENERGY AND THE MAGNITUDE OF EUCLIDEAN DOMAINS

Gimperlein, Heiko and Goffeng, Magnus LU orcid (2023) In Proceedings of the American Mathematical Society 151(2). p.897-906
Abstract

We study the geometric significance of Leinster’s notion of magnitude for a compact metric space. For a smooth, compact domain X in an odd-dimensional Euclidean space, we show that the asymptotic expansion of the function MX(R) = Mag(R·X) at R = ∞ determines the Willmore energy of the boundary ∂X. This disproves the Leinster-Willerton conjecture for a compact convex body in odd dimensions.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the American Mathematical Society
volume
151
issue
2
pages
10 pages
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85144725478
ISSN
0002-9939
DOI
10.1090/proc/16163
language
English
LU publication?
yes
id
b757ed77-1081-464b-85e7-c14b01c4e31b
date added to LUP
2023-02-02 10:28:59
date last changed
2025-10-14 10:50:44
@article{b757ed77-1081-464b-85e7-c14b01c4e31b,
  abstract     = {{<p>We study the geometric significance of Leinster’s notion of magnitude for a compact metric space. For a smooth, compact domain X in an odd-dimensional Euclidean space, we show that the asymptotic expansion of the function M<sub>X</sub>(R) = Mag(R·X) at R = ∞ determines the Willmore energy of the boundary ∂X. This disproves the Leinster-Willerton conjecture for a compact convex body in odd dimensions.</p>}},
  author       = {{Gimperlein, Heiko and Goffeng, Magnus}},
  issn         = {{0002-9939}},
  language     = {{eng}},
  month        = {{02}},
  number       = {{2}},
  pages        = {{897--906}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Proceedings of the American Mathematical Society}},
  title        = {{THE WILLMORE ENERGY AND THE MAGNITUDE OF EUCLIDEAN DOMAINS}},
  url          = {{http://dx.doi.org/10.1090/proc/16163}},
  doi          = {{10.1090/proc/16163}},
  volume       = {{151}},
  year         = {{2023}},
}