Qiang Tu

activity

20242026

collaborators

7 papers

math.AP2026

The existence of $(p, k)$ -convex hypersurfaces for a class of Hessian quotient type curvature equations

Jiabao Gong, Qiang Tu

This article investigates the existence of closed, star-shaped hypersurfaces for a class of Hessian quotient type curvature equations, in which the operator $\frac{σ _{k}}{σ _{l}} (Λ)$ ar…

math.AP2026

The $L_{p}$ dual Christoffel-Minkowski type problem for a class of Hessian quotient equations

Shasha Luo, Jiabao Gong, Qiang Tu

In this paper, we investigate an $L_{p}$ dual Christoffel-Minkowski type problem for the Hessian quotient operator $\frac{σ _{k} ( Λ )}{σ _{l} ( Λ )}$ , where the operator $Λ$ has been widely…

math.AP2026

The Neumann problem for a class of degenerate Hessian quotient type equations

Jiabao Gong, Qiang Tu

In this paper, we obtain some important inequalities for a class of Hessian quotient type operators $\frac{σ _{k} ( Λ ( D ^{2} u ))}{σ _{l} ( Λ ( D ^{2} u ))}$ , which can be regarded as a generalization o…

math.AP2025

The $L_{p}$ -dual Christoffel-Minkowski problem for the case $p \geq q$

Xiaojuan Chen, Qiang Tu, Ni Xiang

In this paper, we consider a class of Hessian equations associated to the $L_{p}$ -dual Christoffel-Minkowski problem for the case $p \geq q$ . By combining the tools of constant rank t…

math.AP2025

Second order estimates for $χ$ -semi convex solutions of Hessian equations on Hermitian manifolds

Xiaojuan Chen, Qiang Tu, Ni Xiang

In this paper, we establish the modified concavity inequality for complex Hessian equations under the semi-convexity assumption inspired by Lu \cite{Lu23} and Zhang \cite{Z24} for…

math.AP2024

$k$ -convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds

Xiaojuan Chen, Qiang Tu, Ni Xiang

In this paper, we consider Weingarten curvature equations for $k$ -convex hypersurfaces with $n < 2 k$ in a warped product manifold $M = I \times_{λ} M$ . Based on the conjecture p…

math.AP2024

Dirichlet problem for degenerate Hessian quotient type curvature equations

Xiaojuan Chen, Qiang Tu, Ni Xiang

In the paper, we prove the existence and uniqueness results of the $C^{1, 1}$ regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curva…

The existence of (p,k)-convex hypersurfaces for a class of Hessian quotient type curvature equations

The Lp​ dual Christoffel-Minkowski type problem for a class of Hessian quotient equations

The Neumann problem for a class of degenerate Hessian quotient type equations

The Lp​-dual Christoffel-Minkowski problem for the case p≥q

Second order estimates for χ-semi convex solutions of Hessian equations on Hermitian manifolds

k-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds

Dirichlet problem for degenerate Hessian quotient type curvature equations

The existence of $(p, k)$ -convex hypersurfaces for a class of Hessian quotient type curvature equations

The $L_{p}$ dual Christoffel-Minkowski type problem for a class of Hessian quotient equations

The $L_{p}$ -dual Christoffel-Minkowski problem for the case $p \geq q$

Second order estimates for $χ$ -semi convex solutions of Hessian equations on Hermitian manifolds

$k$ -convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds