Non-unique conical and non-conical tangents to rectifiable stationary varifolds in ℝ4

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  • Institute of Mathematics, Czech Academy of Sciences


We construct a rectifiable stationary 2-varifold in ℝ4 with non-conical, and hence non-unique, tangent varifold at a point. This answers a question of Simon (Lectures on geometric measure theory, p 243, 1983) and provides a new example for a related question of Allard (Ann Math (2) 95(3):417–491, 1972, p 460). There is also a (rectifiable) stationary 2-varifold in ℝ4 that has more than one conical tangent varifold at a point.


Original languageEnglish
Pages (from-to)1875-1909
Number of pages35
JournalCalculus of Variations and Partial Differential Equations
Issue number2
Early online date28 May 2015
Publication statusPublished - 22 Oct 2015


  • 28A75, 35B65, 49Q20

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