On a conjecture of Almgren: area-minimizing submanifolds with fractal singularities

2021/10/25 by Liu, Zhenhua · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.13137

Abstract

We construct area-minimizing submanifolds with fractal singular sets on compact Riemannian manifolds. Thus, we settle a conjecture by Almgren and our answer is sharp dimensionwise. Furthermore, we can prescribe arbitrarily the strata in the Almgren stratification of the singular sets of our area-minimizing submanifolds, and our results hold in the category of integral currents, mod v currents and stable stationary varifolds.

Cited by

• Special Lagrangians with multiple isolated singularities
• The Hasse Principle for Geometric Variational Problems: An Illustration via Area-minimizing Submanifolds

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