We prove that a harmonic quasiconformal mapping defined on finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits extension to whole plane if its Schwarzian derivative is small. also make observation univalence criterion for mappings holds uniform domains.

We formulate $\lambda$-deformed $\sigma$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly deformation parameter $\lambda$ for large values level $k$ underlying WZW model. To perform our computations use either conformal perturbation theory association with Cardy's doubling trick, well meromorphi...