On a Problem Posed by Brezis and Mironescu
Analysis of PDEs
2026-03-10 v1 Differential Geometry
Abstract
The purpose of this note is to present a positive answer to an open problem proposed in the recent book \cite{Brezis-Mironescu} by H. Brezis and P. Mironescu. It has been stated in this book {\it Sobolev Maps to the Circle} as Proposition 4.3. We demonstrate, in particular, the value of the least mass of the area minimizing integral rectifiable currents with a given boundary equals to the infimum of areas among smoothly immersed submanifolds with the same boundary, under the assumption that the boundary is that of a smooth submanifold.
Cite
@article{arxiv.2603.07877,
title = {On a Problem Posed by Brezis and Mironescu},
author = {Fanghua Lin and Malkeil Shoshan and Changyou Wang},
journal= {arXiv preprint arXiv:2603.07877},
year = {2026}
}
Comments
14 pages, along with 5 figures