调和Q值映射奇点的可整流性和上Minkowski界

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

摘要

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。

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

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 $Q$.

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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.