Author

Guo-Huan Qiu

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Preprint Sep 2026

Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

We resolve the long-standing problem of establishing interior $C^2$ estimates for admissible solutions of the graphical scalar curvature equation in every dimension $n\ge 3$. More precisely, we prove interior curvature estimates for admissible solutions to the constant graphical scalar curvature equation. The proof...

Guo-Huan Qiu, Jin Yan · 3 citations

Preprint Aug 2026

A Brunn--Minkowski inequality and Convexity for the 2-Hessian eigenvalue in convex domains

We prove the strict log-concavity of the positive first eigenfunction $-u$ of the $2$-Hessian equation and the strict $1/2$-convexity of the solution for the corresponding torsion problem in smooth bounded uniformly convex domains in $\mathbb{R}^{n}$. As applications, we establish the associated Brunn--Minkowski in...

Jia-Huan Li, Xi-Nan Ma, Guo-Huan Qiu et al. · 1 citation · ⚡1