Almost all Lagrangian torus orbits in \mathbb CPⁿ are not Hamiltonian volume minimizing

2015/12/07 by Iriyeh, Hiroshi, Ono, Hajime
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53D12 #Secondary 53D10 #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1512.01940

Abstract

All principal orbits of the standard Hamiltonian Tⁿ-action on the complex projective space \mathbb CPⁿ are Lagrangian tori.In this article, we prove that most of them are not volume minimizing under Hamiltonian isotopies of \mathbb CPⁿ if the complex dimension n is greater than two, although they are Hamiltonian minimal and Hamiltonian stable.

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