A special concavity property for positive Hessian quotient operators

Published 19 Sep 2025 in math.AP and math.DG | (2509.16406v1)

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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