Real-analytic continuation along a fixed direction

This talk is devoted to studying analytic continuations of functions of several variables that are $\mathbb R$-analytic along a fixed direction. The presented results have direct relation with the well-known Hartogs theorem on the analyticity of separately-analytic functions in multidimensional complex analysis. However, their studies is significantly different. In this work, the main method for studying continuations of $\mathbb R$-analytic functions is based on the use of the rich properties of analytic functions of several variables and the pluripotential theory based on the Monge–Ampere operator $(dd^cu)^n$.