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

Jan Kolar

doi:10.1007/s00526-015-0847-9

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

Jan Kolar

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1875-1909
Number of pages	35
Journal	Calculus of Variations and Partial Differential Equations
Volume	54
Issue number	2
Early online date	28 May 2015
DOIs	https://doi.org/10.1007/s00526-015-0847-9
Publication status	Published - 22 Oct 2015

Keywords

28A75
35B65
49Q20

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s00526-015-0847-9Licence: None: All rights reserved

https://link.springer.com/content/pdf/10.1007%2Fs00526-015-0847-9.pdfLicence: Unspecified

Cite this

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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.",

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AB - 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.

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