Oh's conjecture on Hamiltonian volume minimization of product tori

Let T(b)=T(b1,,bn)=S1(b1)××S1(bn)CnT(\boldsymbol{b})=T(b_1,\ldots,b_n)=S^1(b_1)\times\cdots\times S^1(b_n)\subset\mathbb C^n be the product Lagrangian torus, where each bi>0b_i>0 and S1(bi)S^1(b_i) is the circle bounding a disc of area bib_i.

Oh's conjecture. The Lagrangian torus T(b)T(\boldsymbol{b}) in Cn\mathbb C^n is Hamiltonian volume minimizing.

The claim would extend the one-dimensional isoperimetric inequality to product Lagrangian tori. The source presents it as a conjecture based on the Hamiltonian minimality and Hamiltonian stability of these tori, but the supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Hiroshi Iriyeh and Hajime Ono, “Almost all Lagrangian torus orbits in CP^n are not Hamiltonian volume minimizing”, arXiv:1512.01940 (2015).

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