6 papers
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…
Creep Behavior of High-Entropy Alloys: A Critical Review
Mingwei Zhang, Uwe Glatzel, Martin Heilmaier +1
High-entropy alloys (HEAs) comprise a compositionally complex class of materials that in certain cases exhibit outstanding mechanical properties. While substantial progress has bee…
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…