Solutions to the minimal surface system with large singular sets

Autor:	Mooney, Connor, Savin, Ovidiu
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Lawson and Osserman proved that the Dirichlet problem for the minimal surface system is not always solvable in the class of Lipschitz maps. However, it is known that minimizing sequences (for area) of Lipschitz graphs converge to objects called Cartesian currents. Essentially nothing is known about these limits. We show that such limits can have surprisingly large interior vertical and non-minimal portions. This demonstrates a striking discrepancy between the parametric and non-parametric area minimization problems in higher codimension. Moreover, our construction has the smallest possible dimension ($n = 3$) and codimension $(m = 2)$. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.14376 Zobrazit plný text záznamu View this record from Arxiv