Convergence of Hermitian-Yang-Mills connections on two-dimensional Kähler tori and mirror symmetry (Q830406)

The main goal of the paper under review is to study the limiting behavior of a family of Hermitian-Yang-Mills connections on a complex two-dimensional Kähler torus when the metric on it goes to the adiabatic limit. The author proves a convergence theorem of connections for this family. Through this analysis and based on the idea of mirror symmetry, the author shows a natural construction of (special) Lagrangian submanifolds on the mirror torus. This conjecturally provides the inverse of the homological mirror symmetry construction [\textit{K. Fukaya}, J. Algebr. Geom. 11, No. 3, 393--512 (2002; Zbl 1002.14014)].