Metric currents and Alberti representations

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• 作者：Andrea Schioppa ^{andrea.schioppa@math.ethz.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53C23 ; 49Q15
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：271
• 期：11
• 页码：3007-3081
• 全文大小：964 K

文摘

We relate Ambrosio–Kirchheim metric currents to Alberti representations and Weaver derivations. In particular, given a metric current m>T  m>, we show that if the module mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616302324&_mathId=si1.gif&_user=111111111&_pii=S0022123616302324&_rdoc=1&_issn=00221236&md5=de0703c38b0b9aa236713c90ae1f65fb" title="Click to view the MathML source">X(‖T‖)mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mi mathvariant="script">Xmi><mo stretchy="false">(mo><mo stretchy="false">‖mo><mi>Tmi><mo stretchy="false">‖mo><mo stretchy="false">)mo>math> of Weaver derivations is finitely generated, then m>Tm> can be represented in terms of derivations; this extends previous results of Williams. Applications of this theory include an approximation of 1-dimensional metric currents in terms of normal currents and the construction of Alberti representations in the directions of vector fields.