On a class of Hessian quotient type equations on Riemannian manifolds

Abstract

Jiao-Liu [Proc. Amer. Math. Soc. 151 (2023), pp. 569–581] proved the existence and the uniqueness of solutions for a class of k-Hessian equations on Riemannian manifolds using the continuity method. In this article, we use the results of Chen et al. [Calc. Var. Partial Differential Equations 62 (2023), p. 15] to extend their results to the corresponding Hessian quotient equations on Riemannian manifolds.