Marcin Sroka

collaborators

4 papers

math.AP2026

On Liouville's theorem for the Hessian quotient equation $I ¨ _{2} / I ¨ _{1}$

Siyuan Lu, Marcin Sroka

We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation $I ¨ _{2} / I ¨ _{1} = 1$ in $R^{n}$ . The proof is based on the observation that after rewriti…

math.AP2025

A special concavity property for positive Hessian quotient operators

Pengfei Guan, Marcin Sroka

We establish a special concavity property for positive Hessian quotient operators $\frac{I ¨ _{n} ( W )}{I ¨ _{n - k} ( W )}, 1 \leq k \leq n - 1$ . As a consequence, we prove a Jacobi inequality for…

math.CV2025

A priori estimates for the complex Monge-AmpÃ¨re equation after Krylov

SÅawomir Dinew, Marcin Sroka

We establish an analytic proof for the Krylov $C^{1, 1}$ estimates for solutions of degenerate complex Monge-AmpÃ¨re equation. We also provide an analytic proof of the Bedford-Taylo…

math.DG2025

Remarks on Hessian quotient equations on Riemannian manifolds