Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity

Author(s)

Nardulli, Stefano ; Resende, Reinaldo

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 455, p. 78-pg., 2024-08-21.

Abstract

In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d d area minimizing currents, beyond that, several results are stated in the more general context of ( C 0 , alpha 0, 0 , r 0 )-almost area minimizing currents of arbitrary dimension m and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes one-sided and two-sided points, of any 2d d area minimizing current T is an open dense set in the boundary. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/). (AU)

• FAPESP's process: 21/05256-0 - Geometric variational problems: existence, regularity and geometrical characterization of the solutions
• Grantee: Stefano Nardulli
• Support Opportunities: Research Grants - Young Investigators Grants