标题： 二维不可约的Ginzburg--Landau场 显示英文标题

标题： Irreducible Ginzburg--Landau fields in dimension 2

摘要： Ginzburg--Landau场是Ginzburg--Landau自由能变分方程的解，该自由能依赖于两个正参数$\alpha$和$\beta$。我们给出了$\alpha$和$\beta$的条件，以保证这些方程不可约解的存在性。我们的结果适用于任何紧致、定向、黎曼2流形（例如平面中的区域，闭合定向曲面），具有de Gennes--Neumann边界条件。我们还证明了，对于每个这样的$\Sigma$以及所有$\alpha$和$\beta$，Ginzburg--Landau场仅在有限个能量值下存在。我们通过使用Feehan和Maridakis的一个结果，并证明Ginzburg--Landau自由能在规范轨道空间上是一个正常函数来证明这一点。 显示英文摘要

摘要： Ginzburg--Landau fields are solutions of the variational equations of the Ginzburg--Landau free energy, which depends 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 any compact, oriented, Riemannian 2-manifold (e.g. domains of the plane, closed oriented surfaces) with de Gennes--Neumann boundary conditions. We also prove that, for each such $\Sigma$ and all $\alpha$ and $\beta$, Ginzburg--Landau fields exist for only a finite set of energy values. We prove that by using a result of Feehan and Maridakis and showing that the Ginzburg--Landau free energy is a proper function on the space of gauge orbits.