Multidimensional complex analysis

Multidimensional complex analysis is a branch of mathematics that studies holomorphic functions of several complex variables defined in a multidimensional complex space, holomorphic mappings, and subvarieties of the complex space. The beginning of a systematic study of multidimensional complex functions was laid by K. Weierstrass and A. Poincaré at the end of the XIX century. A. Poincaré extended the Cauchy main theorem to functions of several variables and laid the foundations of the multidimensional theory of residues. Methods of multidimensional complex analysis are currently widely used in quantum field theory, mathematical physics, differential and algebraic geometry.