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.
|Number of pages||35|
|Journal||Calculus of Variations and Partial Differential Equations|
|Early online date||28 May 2015|
|Publication status||Published - 22 Oct 2015|
ASJC Scopus subject areas
- Applied Mathematics