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

Jan Kolar

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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
Volume54
Issue number2
Early online date28 May 2015
DOIs
Publication statusPublished - 22 Oct 2015

Keywords

  • 28A75
  • 35B65
  • 49Q20

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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