ISSN:
1420-8903
Keywords:
52A20
;
49F10
;
53C42
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 Λ 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 Φ more general than area. One result implies that form-dimensional surfaces inR n , with 2 ⩽m ⩽n − 2, for any integrand Φ, there are Φ-minimizing surfaces with interior singularities.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01840470
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