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

DOI10.1007/S00526-015-0847-9zbMATH Open1327.28006arXiv1303.3677OpenAlexW3102829537MaRDI QIDQ745573

Jan Kolár

Publication date: 14 October 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Abstract: We construct a rectifiable stationary 2-varifold in R^4 with non-conical, and hence non-unique, tangent varifold at a point. This answers a question of L. Simon (Lectures on geometric measure theory, 1983, p. 243) and provides a new example for a related question of W.K. Allard (On the first variation of a varifold, Ann. of Math., 1972, p. 460). There is also a (rectifiable) stationary 2-varifold in R^4 that has more than one conical tangent varifold at a point. keywords: stationary varifold, varifold tangent, tangent cone, non-unique, non-conical, minimal surface, regularity

Full work available at URL: https://arxiv.org/abs/1303.3677

zbMATH Keywords

varifoldconical tangentnon-conical tangent

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75)

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