The Willmore Functional on Lagrangian Tori: Its Relation to Area and Existence of Smooth Minimizers

1995 ◽  
Vol 8 (4) ◽  
pp. 761 ◽  
Author(s):  
William P. Minicozzi II
Keyword(s):  
Willmore Functional ◽  
Lagrangian Tori

scholarly journals Lagrangian tori in closed 4-manifolds

2010 ◽  
Vol 3 (2) ◽  
pp. 333-342
Author(s):  
Adam C. Knapp
Keyword(s):  
Lagrangian Tori

scholarly journals Unknottedness of real Lagrangian tori in $$S^2\times S^2$$

2020 ◽  
Vol 378 (3-4) ◽  
pp. 891-905
Author(s):  
Joontae Kim
Keyword(s):  
Lagrangian Tori

scholarly journals Squeezing Lagrangian tori in dimension 4

2020 ◽  
Vol 95 (3) ◽  
pp. 535-567
Author(s):  
Richard Hind ◽  
Emmanuel Opshtein
Keyword(s):  
Lagrangian Tori

Nontoric foliations by Lagrangian tori of toric Fano varieties

2010 ◽  
Vol 87 (1-2) ◽  
pp. 43-51 ◽  
Author(s):  
S. A. Belev ◽  
N. A. Tyurin
Keyword(s):  
Fano Varieties ◽  
Lagrangian Tori ◽  
Toric Fano Varieties

Local minimizers of the Willmore functional

Analysis ◽  
2015 ◽  
Vol 35 (2) ◽  
Author(s):  
Florian Skorzinski
Keyword(s):  
Critical Point ◽  
Local Minimizer ◽  
Positive Definite ◽  
Second Derivative ◽  
Sufficient Condition ◽  
Conformal Transformations ◽  
Willmore Functional ◽  
Local Minimizers

AbstractSince the Willmore functional is invariant with respect to conformal transformations and reparametrizations, the kernel of the second derivative of the functional at a critical point will always contain a subspace generated by these transformations. We prove that the second derivative being positive definite outside this space is a sufficient condition for a critical point to be a local minimizer.

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