Solution of the boundary value problem of determining the axisymmetric equilibrium surface of a liquid under weak gravity conditions

The paper studies an algorithm for constructing the axisymmetric equilibrium surface of a liquid under weak gravity with allowance for surface tension. Existence of a solution is studied, and determination of the solution of the boundary value problem is reduced to solving transcendental equations, whose real solution is found in the form of power series. Numerical calculations for vessels with different geometric forms are presented.