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Abstract: : It is shown that every stationary polyhedral set in Euclidean space is area minimizing under diffeomorphisms leaving the boundary fixed. Similar theorems are also proved for crystals and immiscible fluids. There are infinitely many minimal cones in R 3 . Of these only three are area minimizing under Lipschitz maps: the plane; the three half planes meeting along their common boundary line at an angle of 120 degrees; the cone over the one-skeleton of the regular tetrahedron (see [T]). A... (Update)
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BibTeX entry: (Update)
@misc{ choe-every,
author = "Jaigyoung Choe",
title = "Every Stationary Polyhedral Set in R^n is Area Minimizing under Diffeomorphisms",
url = "citeseer.ist.psu.edu/408147.html" }
Citations (may not include all citations):8 Minimal varieties in riemannian manifolds (context) - Simons - 1968
3 Paired calibrations applied to soapfilms (context) - Lawlor, Morgan
2 Minimal cones on hypercubes (context) - Brakke - 1991
1 489--539 (context) - Taylor, of et al. - 1976
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