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Rectangular constrained Willmore minimizers and the Willmore conjecture | Lynn Heller
; Sebastian Heller
; Cheikh Birahim Ndiaye
; | Date: |
17 Jan 2019 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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