English

A special concavity property for positive Hessian quotient operators

Analysis of PDEs 2025-09-23 v1 Differential Geometry

Abstract

We establish a special concavity property for positive Hessian quotient operators σn(W)σnk(W), 1kn1\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.

Keywords

Cite

@article{arxiv.2509.16406,
  title  = {A special concavity property for positive Hessian quotient operators},
  author = {Pengfei Guan and Marcin Sroka},
  journal= {arXiv preprint arXiv:2509.16406},
  year   = {2025}
}