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This paper gives a new way of constructing Landau-Ginzburg mirrors usingdeformation theory of Lagrangian immersions motivated by the works of Seidel,Strominger-Yau-Zaslow and Fukaya-Oh-Ohta-Ono. Moreover we construct a canonicalfunctor from the Fukaya category to the mirror category of matrixfactorizations. This functor derives homological mirror symmetry under someexplicit assumptions.  As an application, the construction is applied to spheres with three orbifoldpoints to produce their quantum-corrected mirrors and derive homological mirrorsymmetry. Furthermore we discover an enumerative meaning of the (inverse)mirror map for elliptic curve quotients.

Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}