Wei Wei

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math.DG2026

Optimal geometric inequalities and fully nonlinear conformal flows

Yuxin Ge, Guofang Wang, Wei Wei

We establish sharp Sobolev-type geometric inequalities on $S^{n}$ involving the total $σ_{k}$ -curvatures $\int_{S^{n}} σ_{k} (g) d v_{g}$ . These results extend the optimal in…

math.DG2026

A new boundary mass for asymptotically flat half-manifolds

Guofang Wang, Wei Wei

We introduce a boundary analogue of the Gauss--Bonnet--Chern mass for asymptotically flat half-manifolds with non-compact boundary. We prove that this mass is well defined and esta…

math.DG2026

The $σ_{k}$ -Yamabe problem revisited

Yuxin Ge, Guofang Wang, Wei Wei

In this paper we revisit the $σ_{k}$ -Yamabe problem on $M^{n}$ , namely, finding a conformal metric with constant $σ_{k}$ -scalar curvature. We prove that on a closed manifold $\left(M,\le…

math.DG2026

Blow-up phenomena for the constant Q/R-curvature equation

Caiyan Li, Guofang Wang, Wei Wei

Let $n \geq 25$ be an integer. In this paper, we construct a Riemannian metric $g_{0}$ on $S^{n}$ , smooth for $n \geq 26$ and of class $C^{9}$ but not $C^{10}$ for $n = 25$ , with t…

math.DG2026

A Yamabe problem for the quotient between the $Q$ curvature and the scalar curvature

Yuxin Ge, Guofang Wang, Wei Wei

In this paper we introduce the following Yamabe problem for the quotient between the $Q$ curvature and the scalar curvature $R$ : Find a conformal metric $g$ in a given conformal cl…

math.DG2024

Liouville Theorem for $k -$ curvature equation in half space with fully nonlinear boundary condition

Wei Wei

We establish the Liouville theorem for positive constant $σ_{k}$ -curvature equation in $R_{+}^{n}$ and positive constant boundary $B_{k}^{g}$ curvature equation,…

Optimal geometric inequalities and fully nonlinear conformal flows

A new boundary mass for asymptotically flat half-manifolds

The σk​-Yamabe problem revisited

Blow-up phenomena for the constant Q/R-curvature equation

A Yamabe problem for the quotient between the Q curvature and the scalar curvature

Liouville Theorem for k−curvature equation in half space with fully nonlinear boundary condition

The $σ_{k}$ -Yamabe problem revisited

A Yamabe problem for the quotient between the $Q$ curvature and the scalar curvature

Liouville Theorem for $k -$ curvature equation in half space with fully nonlinear boundary condition