| Full text | |
| Author(s): |
De Lellis, Camillo
;
Nardulli, Stefano
;
Steinbruchel, Simone
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PUBLICATIONS MATHEMATIQUES DE L IHES; v. 140, n. 1, p. 118-pg., 2024-02-21. |
| Abstract | |
We consider integral area-minimizing 2-dimensional currents T in U subset of R2+n with partial derivative T = Q parallel to Gamma parallel to, where Q is an element of N\{0} and Gamma is sufficiently smooth. We prove that, if q is an element of Gamma is a point where the density of T is strictly below Q+1/2, then the current is regular at q. The regularity is understood in the following sense: there is a neighborhood of q in which T consists of a finite number of regular minimal submanifolds meeting transversally at Gamma (and counted with the appropriate integer multiplicity). In view of well-known examples, our result is optimal, and it is the first nontrivial generalization of a classical theorem of Allard for Q = 1. As a corollary, if Omega subset of R2+n is a bounded uniformly convex set and Gamma subset of partial derivative Omega a smooth 1-dimensional closed submanifold, then any area-minimizing current T with partial derivative T = Q parallel to Gamma parallel to is regular in a neighborhood of Gamma. (AU) | |
| FAPESP's process: | 18/22938-4 - Boundary regularity for area minimizing currents |
| Grantee: | Stefano Nardulli |
| Support Opportunities: | Scholarships abroad - Research |
| 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 |