Ni Xiang

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math.AP2025

Second order estimates for $I ¨ $ -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.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.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 $M = I \times_{I^} » M$ . Based on the conjecture…

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…

Second order estimates for I¨-semi convex solutions of Hessian equations on Hermitian manifolds

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

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

Dirichlet problem for degenerate Hessian quotient type curvature equations

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

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

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