Non-unique conical and non-conical tangents to rectifiable stationary varifolds in \(\mathbb R^4\)

  • Jan KolářEmail author


We construct a rectifiable stationary 2-varifold in \({\mathbb {R}}^4\) 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 \({\mathbb {R}}^{4}\) that has more than one conical tangent varifold at a point.

Mathematics Subject Classification

28A75 49Q20 35B65 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of MathematicsCzech Academy of SciencesPrague 1Czech Republic

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