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

doi:10.3792/pjaa.79.167

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Dec. 2003 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

Proc. Japan Acad. Ser. A Math. Sci. 79(10): 167-170 (Dec. 2003). DOI: 10.3792/pjaa.79.167

Abstract

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.

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Hiroshi Iriyeh. Hajime Ono. Takashi Sakai. "Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in $S^2 \times S^2$." Proc. Japan Acad. Ser. A Math. Sci. 79 (10) 167 - 170, Dec. 2003. https://doi.org/10.3792/pjaa.79.167