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arXiv · 2509.16406

A special concavity property for positive Hessian quotient operators

Pengfei Guan·Marcin Sroka
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Abstract

We establish a special concavity property for positive Hessian quotient operators $\frac{\sigma_n(W)}{\sigma_{n-k}(W)}, \ 1\le k\le n-1$. As a consequence, we prove a Jacobi inequality for general symmetric tensor satisfying positive Hessian quotient equation on Riemannian manifolds.

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Pengfei Guan, Marcin Sroka. 2025-09-19. A special concavity property for positive Hessian quotient operators. https://doi.org/10.3934/dcds.2025181

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