Over-determined problems for kk-Hessian equations in ring-shaped domains

In this paper, we firstly use a variant of the moving plane method of Alexandroff to obtain radial symmetry of solutions for kk-Hessian equations in annulus-type domains, which can be regarded as a generalization of Gidas–Ni–Nirenberg result in 1979. Then we consider an over-determined problem for kk-Hessian equations in ring-shaped domains and prove the radial symmetry of the solutions and the domains.