Journal article
UNIQUENESS OF CLIFFORD TORUS WITH PRESCRIBED ISOPERIMETRIC RATIO
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v 150(4), p1749
Apr 2022
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
The Marques-Neves theorem asserts that among all the torodial (i.e. genus 1) closed surfaces, the Clifford torus has the minimal Willmore energy integral H-2 dA. Since the Willmore energy is invariant under Mobius transformations, it can be shown that there is a one-parameter family, up to homotheties, of genus 1 Willmore minimizers. It is then a natural conjecture that such a minimizer is unique if one prescribes its isoperimetric ratio. In this article, we show that this conjecture can be reduced to the positivity question of a polynomial recurrence. A proof of the positivity can be found in the companion article by Melczer and Mezzarobba [submitted to J. Comb. Theory (2020)]. This establishes a first uniqueness result for the Canham model of biomembranes.
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Details
- Title
- UNIQUENESS OF CLIFFORD TORUS WITH PRESCRIBED ISOPERIMETRIC RATIO
- Publication Details
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v 150(4), p1749
- Publisher
- AMER MATHEMATICAL SOC; PROVIDENCE
- Grant note
- The first author was supported in part by the National Science Foundation grants DMS 0512673 and DMS 0915068. This work was partially supported by NSF grants DMS 0915068 and DMS 1115915.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:000768808400035
- Scopus ID
- 2-s2.0-85124616110
- Other Identifier
- 991021861205604721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied