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28 March 2024
 
  » arxiv » 1901.5664

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Rectangular constrained Willmore minimizers and the Willmore conjecture
Lynn Heller ; Sebastian Heller ; Cheikh Birahim Ndiaye ;
Date 17 Jan 2019
AbstractWe show that the well-known family of $2$-lobed Delaunay tori $;f^b;$ in $;S^3,;$ parametrized by $;b in mathbb R_{geq1},;$ uniquely minimizes the Willmore energy among all immersions from tori into $3$-space of conformal class $;(a, b);$. As a corollary we obtain an alternate proof of the Willmore conjecture in $3$-space. This new strategy can be generalized to arbitrary codimensions provided a classification of isothermic constrained Willmore tori is possible and all $;f^b;$ remain stable in all codimensions.
Source arXiv, 1901.5664
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