Minimal submanifolds from the abelian Higgs model

• 成果类型: Article
• 署名作者: Pigati, Alessandro; Stern, Daniel
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-01000-6
• 发表日期: 2021
• 页码: 1027-1095
• 关键词: phase-transitions; CONVERGENCE; interfaces; van; 1st

摘要

Given a Hermitian line bundle L -> M over a closed, oriented Riemannian manifoldM, we study the asymptotic behavior, as epsilon -> 0, of couples(u(epsilon), del(epsilon)) critical for the rescalings E epsilon(u, del)= (M)integral(vertical bar del u vertical bar(2)+epsilon(2)vertical bar F-del vertical bar(2)+1/4 epsilon(2)(1-vertical bar u vertical bar(2))(2)) of the self-dual Yang-Mills-Higgs energy, whereuis a section of Land del is a Hermitian connection on L with curvature F-del. Under the natural assumptionlim sup epsilon -> 0 E-epsilon(u(epsilon), del(epsilon))