Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps

IF 1.1 3区数学 Q1 MATHEMATICS Commentarii Mathematici Helvetici Pub Date : 2016-12-06 DOI:10.4171/CMH/449

Camillo De Lellis, Andrea Marchese, E. Spadaro, Daniele Valtorta

引用次数: 28

Abstract

In this article we prove that the singular set of Dirichlet-minimizing $Q$-valued functions is countably $(m-2)$-rectifiable and we give upper bounds for the $(m-2)$-dimensional Minkowski content of the set of singular points with multiplicity $Q$.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

调和Q值映射奇点的可整流性和上Minkowski界

本文证明了dirichlet - miniming$ Q$值函数的奇异集是可可数的$(m-2)$可整形的，并给出了具有多重性$Q$的奇点集的$(m-2)$维Minkowski内容的上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.

期刊最新文献

Staircase patterns in Hirzebruch surfaces On the asymptotic growth of Birkhoff integrals for locally Hamiltonian flows and ergodicity of their extensions Area and Gauss–Bonnet inequalities with scalar curvature Non-planarity of Markoff graphs $\bmod~p$ Non-planarity of Markoff graphs $\bmod~p$