THE WILLMORE ENERGY AND THE MAGNITUDE OF EUCLIDEAN DOMAINS
(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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https://lup.lub.lu.se/record/b757ed77-1081-464b-85e7-c14b01c4e31b
- author
- Gimperlein, Heiko and Goffeng, Magnus LU
- organization
- publishing date
- 2023-02-01
- 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
- 2023-02-02 10:28:59
@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}}, }