Marcin Sroka

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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…

On Liouville's theorem for the Hessian quotient equation I¨2​/I¨1​

A special concavity property for positive Hessian quotient operators

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