Author

Guo-Huan Qiu

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Preprint Aug 2026

Robin and Neumann problems for the graph scalar curvature equation

We study Robin and Neumann problems for the scalar curvature equation of admissible graphs over bounded uniformly convex domains in three dimensions. Under a small-volume assumption, we prove existence and uniqueness for the Robin problem and obtain a classical Neumann solution as the Robin parameter tends to zero. The...

Guo-Huan Qiu · 1 citation

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 · 6 citations · ⚡2

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