Almgren and topological minimality for the set Y×Y

Xiangyu Liang

doi:10.1016/j.jfa.2014.02.033

Almgren and topological minimality for the set Y×Y

Xiangyu Liang^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper we discuss various minimality properties for the orthogonal product of two 1-dimensional Y sets, and some related problems. This is motivated by an attempt to give the classification of singularities for 2-dimensional Almgren-minimal sets in R4. The key of the proof is to find a new way to apply the method of paired calibration, which only worked in codimension 1, to our special set of codimension larger than 1.

Original language	English
Pages (from-to)	6007-6054
Number of pages	48
Journal	Journal of Functional Analysis
Volume	266
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2014.02.033
State	Published - 15 May 2014

Keywords

Classification of singularities
Hausdorff measure
Minimal sets
Paired calibrations for higher codimension
Topological decomposition

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10.1016/j.jfa.2014.02.033

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abstract = "In this paper we discuss various minimality properties for the orthogonal product of two 1-dimensional Y sets, and some related problems. This is motivated by an attempt to give the classification of singularities for 2-dimensional Almgren-minimal sets in R4. The key of the proof is to find a new way to apply the method of paired calibration, which only worked in codimension 1, to our special set of codimension larger than 1.",

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AB - In this paper we discuss various minimality properties for the orthogonal product of two 1-dimensional Y sets, and some related problems. This is motivated by an attempt to give the classification of singularities for 2-dimensional Almgren-minimal sets in R4. The key of the proof is to find a new way to apply the method of paired calibration, which only worked in codimension 1, to our special set of codimension larger than 1.

KW - Classification of singularities

KW - Hausdorff measure

KW - Minimal sets

KW - Paired calibrations for higher codimension

KW - Topological decomposition

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ER -

Almgren and topological minimality for the set Y×Y

Abstract

Keywords

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