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Minimal and H-minimal submanifolds in toric geometry. (English) Zbl 1351.53097
A submanifold is minimal if and only if its volume is stationary under all possible variations. A generalisation of this, adapted to the framework of Lagrangian immersions, is the notion of $$H$$-minimal (or Hamiltonian-minimal). In this case the volume of the submanifold is minimal under all Hamiltonian deformations (i.e., deformations which preserve the Lagrangian character of the submanifold). In this paper, following the work of Mironov, the author uses the moment angle manifolds in order to study a special family of Hamiltonian minimal Lagrangian submanifolds.
##### MSC:
 53D12 Lagrangian submanifolds; Maslov index
##### Keywords:
Lagrangian submanifolds; torii; complex space forms
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