Unique tangent behavior for 1-dimensional stationary varifolds

We prove that, without any assumption on lower density bound or codimension, any 1-dimensional stationary varifold on any Riemannian manifold admits unique tangent behavior everywhere. On montre que, sans hypothèse sur la borne inférieure des densités ou la codimension, tout varifold stationnaire de...

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Bibliographic Details
Published inJournal de mathématiques pures et appliquées Vol. 108; no. 5; pp. 633 - 661
Main Author Liang, Xiangyu
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.11.2017
Elsevier
Subjects
Mathematics
Projection
Stationary varifold
Tangent varifold
Uniqueness
28A75
Tangent varifold
49Q15
Uniqueness
Stationary varifold
Projection
49Q20
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Summary:We prove that, without any assumption on lower density bound or codimension, any 1-dimensional stationary varifold on any Riemannian manifold admits unique tangent behavior everywhere. On montre que, sans hypothèse sur la borne inférieure des densités ou la codimension, tout varifold stationnaire de dimension 1 sur toute variété riemannienne admet un cône tangent unique partout.
ISSN:0021-7824
DOI:10.1016/j.matpur.2017.05.011