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Remarks on Hessian quotient equations on Riemannian manifolds by Sroka, Marcin is a scholarly article available to read on EtoBox.

What is Remarks on Hessian quotient equations on Riemannian manifolds about?

We consider Hessian quotient equations in Riemannian setting related to a problem posed by Delano\"e 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.

Author

Sroka, Marcin

Published

2025

Language

EN