English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This short note is the announcement of a forthcoming work in which we prove afirst general boundary regularity result for area-minimizing currents in highercodimension, without any geometric assumption on the boundary, except that itis an embedded submanifold of a Riemannian manifold, with a mild amount ofsmoothness ($C^{3, a_0}$ for a positive $a_0$ suffices). Our theorem allows toanswer a question posed by Almgren at the end of his Big Regularity Paper. Inthis note we discuss the ideas of the proof and we also announce a theoremwhich shows that the boundary regularity is in general weaker that the interiorregularity. Moreover we remark an interesting elementary byproduct on boundarymonotonicity formulae.

Boundary regularity of mass-minimizing integral currents and a question of Almgren