标题： 二维不可约Ginzburg-Landau场 显示英文标题

标题： Irreducible Ginzburg-Landau fields in dimension 2

摘要： Ginburg-Landau场是依赖于两个正参数$\alpha$和$\beta$的Ginburg-Landau方程的解。我们给出了$\alpha$和$\beta$的条件以保证这些方程的不可约解的存在性。我们的结果适用于任意紧致、定向的黎曼二维流形（例如，$\mathbb{R}^2$中有界的区域、球面、环面等）以及de Gennes-Neumann边界条件下。我们还证明了，对于每个这样的流形和所有正的$\alpha$和$\beta$，Ginburg-Landau自由能是等度空间上规范等价类上的Palais-Smale函数，Ginburg-Landau场只存在于有限个能量值上，并且Ginburg-Landau场的模空间是紧致的。 显示英文摘要

摘要： Ginzburg-Landau fields are the solutions of the Ginzburg-Landau equations which depend on two positive parameters, $\alpha$ and $\beta$. We give conditions on $\alpha$ and $\beta$ for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in $\mathbb{R}^2$, spheres, tori, etc.) with de Gennes-Neumann boundary conditions. We also prove that, for each such manifold and all positive $\alpha$ and $\beta$, the Ginzburg-Landau free energy is a Palais-Smale function on the space of gauge equivalence classes, Ginzburg-Landau fields exist for only a finite set of energy values, and the moduli space of Ginzburg-Landau fields is compact.