Calibrations and the size of Grassmann faces |
| |
Authors: | Frank Morgan |
| |
Institution: | (1) Department of Mathematics, Williams College, 01267 Williamstown, MA, USA |
| |
Abstract: | Summary In the past fifteen years or so, convex geometry and the theory of calibrations have provided a deeper understanding of the behavior and singular structure ofm-dimensional area-minimizing surfaces inR
n
. Calibrations correspond to faces of the GrassmannianG(m,R
n
) of orientedm-planes inR
n
, viewed as a compact submanifold of the exterior algebra
m
R
n
. Large faces typically provide many examples of area-minimizing surfaces. This paper studies the sizes of such faces. It also considers integrands more general than area. One result implies that form-dimensional surfaces inR
n
, with 2 m n – 2, for any integrand , there are -minimizing surfaces with interior singularities. |
| |
Keywords: | 52A20 49F10 53C42 |
本文献已被 SpringerLink 等数据库收录! |
|