Remarks on Hessian quotient equations on Riemannian manifolds

We consider Hessian quotient equations in Riemannian setting as appearing in the problem posed by Delano & euml; and Urbas. We prove unobstructed second order a priori estimate for the real Hessian quotient equation via the maximum principle argument on Riemannian manifolds in dimension two. This is achieved by introducing new test function and exploiting some fine concavity properties of quotient operator. This result demonstrates that there is intriguing difference between the real case and the complex case, as there are known obstructions for J-equation in complex geometry. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.