Integral Geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S^2 times S^2

Hiroshi Iriyeh, Hajime Ono, Takashi Sakai

We prove that the product of equators $S^1\times S^1$ in $S^2\times S^2$ is globally volume minimizing under Hamiltonian deformations.