| Affiliation: | (1) Equipe d'analyse harmonique, Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France;(2) Equipe d'analyse harmonique, Mathematics Department - MS136, 6100 S. Main St., TX 77005-1892 Houston, USA |
| Abstract: | We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with  .Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.Received: 11 February 2002, Accepted: 16 June 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 49Q15, 28A75Thierry De Pauw: The research of the first author was supported by a Marie Curie fellowship of the European Community program Human Potential under contract HMPF-CT-2001-01235Robert Hardt: The research of the second author was partially supported by NSF grant DMS-0072486 |
