%0 Journal Article
%T Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type
%A Hiroshi Iriyeh
%A Takashi Sakai
%A Hiroyuki Tasaki
%J Mathematics
%D 2011
%I arXiv
%X In this paper we calculate the Lagrangian Floer homology $HF(L_0, L_1 : {\mathbb Z}_2)$ of a pair of real forms $(L_0,L_1)$ in a monotone Hermitian symmetric space $M$ of compact type in the case where $L_0$ is not necessarily congruent to $L_1$. In particular, we have a generalization of the Arnold-Givental inequality in the case where $M$ is irreducible. As its application, we prove that the totally geodesic Lagrangian sphere in the complex hyperquadric is globally volume minimizing under Hamiltonian deformations.
%U http://arxiv.org/abs/1108.0260v2