On a Problem Posed by Brezis and Mironescu
Abstract
The purpose of this note is to present a positive answer to an open problem proposed in the recent book Brezis-Mironescu by H. Brezis and P. Mironescu. It has been stated in this book 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.
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