7 papers
Harmonic maps from into with least Morse index
Qun Chen, Guofang Wang, Mingwei Zhang
Let be a smooth nonconstant harmonic map. We prove that its Morse index is equal to if and only if \begin{equation*} u = h \circ π\cir…
The curl-Yamabe problem
Guofang Wang, Mingwei Zhang
We introduce and study a Yamabe-type variational problem associated with the curl operator on middle-degree forms on a closed oriented Riemannian manifold with $n\equiv3\…
The sharp curl-Sobolev inequality
Guofang Wang, Mingwei Zhang
We solve a longstanding problem, going back at least to Rivière 1998 and open even in the physically most relevant case , by proving a sharp curl-Sobolev inequality on $\mathb…
On the sharp constants in curl-Sobolev inequalities on
Guofang Wang, Mingwei Zhang
Let and set . On an oriented Riemannian -manifold we consider the (middle-degree) curl operator, $\mathrm{curl}:*\mathrm{d}:Ω^{p}…
Conformal invariants for the zero mode equation
Guofang Wang, Mingwei Zhang
For non-trivial solutions to the zero mode equation on a closed spin manifold \[D φ=iA\cdot φ,\] we first provide a simple proof for the sharp inequality \eq{ \norm{A}_{L^n}^2 \ge…
Stability of spinorial Sobolev inequalities on
Guofang Wang, Mingwei Zhang
The spinorial Sobolev inequality on the unit sphere states \begin{equation*} \Big(\int| Dψ|^{\frac{2n}{n+1}}\Big)^{\frac{n+1}{n}}-\frac{n}{2}ω_{n}^{1/n}\int\langle Dψ,ψ\rangle \geq…