5 papers · 1 filter
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…
A conformal lower bound of weighted Dirac eigenvalues on manifolds with boundary
Mingwei Zhang
For the weighted Dirac eigenproblem on a compact spin manifold with the chiral boundary condition \begin{equation*} \left\{ \begin{array}{ll} DÏ= λfÏ& \text{in } M, \\ \mathbf{B…
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 \[D Ï=iA\cdot Ï,\] we first provide a simple proof for the sharp inequality \eq{ \norm{A}_{L^n}^2 \g…
Stability of spinorial Sobolev inequalities on
Guofang Wang, Mingwei Zhang
The spinorial Sobolev inequality on the unit sphere states \begin{equation*} \Big(\int| DÏ|^{\frac{2n}{n+1}}\Big)^{\frac{n+1}{n}}-\frac{n}{2}Ï_{n}^{1/n}\int\langle DÏ,Ï\rangle…