Author

Jin Yan

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Preprint Sep 2026

The asymptotic Plateau problem for Hypersurfaces of constant $H_{k}$ curvature in hyperbolic space

In this paper, we study the asymptotic Plateau problem in hyperbolic space for hypersurfaces of constant $H_k$-curvature. We prove the existence of a smooth complete $k$-convex hypersurface in $\mathbb{H}^{n+1}$ satisfying \[ H_k(\kappa)=\sigma, \qquad \sigma\in(0,1), \] with prescribed asymptotic boundary at infinity....

Xin-Qun Mei, Jin Yan · 1 citation · ⚡1

Preprint Sep 2026

The $m$-Laplace equation with a gradient term II: classification in the second critical case

Let $1<m<n$ and $0<q<m-1$. We classify positive, locally bounded weak solutions of \[-\Delta_m u=u^p|Du|^q\quad\text{in }\mathbb R^n,\qquad p=\frac{m-q}{n-m}\left(n+\frac{q}{m-1-q}\right)-1.\] Every solution is constant or belongs to an explicit family of radial solutions, up to translation and scaling. No global bound...

Tian Wu, Jin Yan, Hua Zhu · 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 · 3 citations