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arXiv 1503.08330math-phhep-thmath.APmath.MP
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Chern-Simons-Higgs涡旋方程的求解

Resolution of Chern--Simons--Higgs Vortex Equations

Xiaosen Han, Chang-Shou Lin, Yisong Yang

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28 pages
发表信息：
Communications in Mathematical Physics 343 (2016) 701--724
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摘要：

众所周知，当非阿贝尔相对论Chern-Simons-Higgs涡旋方程的Cartan矩阵$K$是一般单李代数的Cartan矩阵时，由于多重约束的存在，使得发展其存在性理论变得困难，迄今为止文献中最强的结果是Cartan子代数是2维的.在本文中，我们克服了这一困难，隐式地解决了多个约束，使用度定理参数，利用一个关键的积极性属性推导出的Cartan矩阵的逆Lusztig和山雀，这使得一个过程中，不等式约束的变分形式主义的等式约束。因此，这项工作建立了一个普遍的存在定理，解决了长期以来在该领域的开放问题，关于一般的可解性方程。

英文摘要：

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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