On conditions of solvability of the Dirichlet problem for $m$-curvature equations

The paper contains the ensharpened variant of the Jenkins–Serrin–Trudinger condition relating to the Dirichlet problem for curvature equations. New condition provides the classical solvability to the Hauss curvature equation in the case of positive curvature, which sufficiently small on the boundary. Bibliography: 8 titles.