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arXiv · 2604.10924

The $L_p$ dual Christoffel-Minkowski type problem for a class of Hessian quotient equations

Shasha Luo·Jiabao Gong·Qiang Tu
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Abstract

In this paper, we investigate an $L_p$ dual Christoffel-Minkowski type problem for the Hessian quotient operator $\frac{\sigma_{k}(\Lambda)}{\sigma_{l}(\Lambda)}$, where the operator $\Lambda$ has been widely studied in the literature. Exploiting the recently discovered ``inverse convexity'' property of this class of operators, we establish a full rank theorem under suitable structural assumptions. Together with a priori estimates, this result enables us to prove the existence and uniqueness of strictly spherically convex solutions to the above $L_p$ dual Christoffel-Minkowski type problem.

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Shasha Luo, Jiabao Gong, Qiang Tu. 2026-04-13. The $L_p$ dual Christoffel-Minkowski type problem for a class of Hessian quotient equations. https://arxiv.org/abs/2604.10924

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