自对偶U(1)‐Yang-Mills-Higgs能量收敛到(n−2)$(n-2)$‐面积泛函

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-09-07 DOI:10.1002/cpa.22150

Davide Parise, Alessandro Pigati, Daniel Stern

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引用次数: 0

摘要

给定封闭黎曼流形上的厄米线束，自对偶的杨-密尔-希格斯能量是一个由截面和厄米连接∇与曲率组成的偶定义的自然泛函族。虽然这些泛函的临界点已经被规范理论界在二维中进行了很好的研究，但在[52]中表明，高维中的临界点收敛于(在适当的意义上)二维的极小子流形，与Allen-Cahn方程和极小超曲面之间的对应关系有很强的相似之处。在本文中，我们通过证明对(2π倍)余维面积的Γ‐收敛来补充这一思想:更准确地说，我们证明了一个合适的规范不变雅可比矩阵收敛于一个积分循环Γ，在与欧拉类对偶的同调类中，具有质量。对于这个同调类中的任何一个积分循环，我们也得到了一个恢复序列。最后，我们应用这些技术比较了Almgren-Pitts理论与Yang-Mills-Higgs框架的最小-最大面积值，表明前者的值总是为后者提供一个下界。作为一种成分，我们还建立了沿梯度流动的Huisken‐型单调性结果。

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Convergence of the self-dual U(1)-Yang–Mills–Higgs energies to the ( n − 2 ) $(n-2)$ -area functional

Given a hermitian line bundle $L \to M$ on a closed Riemannian manifold $(M^{n}, g)$ , the self-dual Yang–Mills–Higgs energies are a natural family of functionals

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.