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Calibrations and the size of Grassmann faces (1992)

Morgan, Frank

Springer

Aequationes mathematicae 43 (1992), S. 1-13

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ISSN: 1420-8903

Schlagwort(e): 52A20 ; 49F10 ; 53C42

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01840470

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