Minimal surfaces, crystals, shortest networks, and undergraduate research

DOI10.1007/BF03025868zbMath0765.52015MaRDI QIDQ1200117

Frank Morgan

Publication date: 17 January 1993

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

zbMATH Keywords

optimizationminimal surfacetetrahedronpolyhedral manifolds

Mathematics Subject Classification ID

Deterministic network models in operations research (90B10) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Statistical mechanics of crystals (82D25) Polyhedral manifolds (52B70)

Related Items (12)

Few distance sets in \(\ell_p\) spaces and \(\ell_p\) product spaces ⋮ Minkowski Geometry—Some Concepts and Recent Developments ⋮ Geometry where direction matters -- or does it? ⋮ The isoperimetrix in the dual Brunn-Minkowski theory ⋮ Extremal problems in Minkowski space related to minimal networks ⋮ Calibrations and the size of Grassmann faces ⋮ The geometry of Minkowski spaces -- a survey. I ⋮ A lower bound for the equilateral number of normed spaces ⋮ An introduction to Minkowski geometries ⋮ Quantitative Illumination of Convex Bodies and Vertex Degrees of Geometric Steiner Minimal Trees ⋮ Cardinalities of \(k\)-distance sets in Minkowski spaces ⋮ Wulff clusters in \(\mathbb{R}^2\)

Cites Work

• The structure of singularities in \(\Phi\)-minimizing networks in \({\mathbb{R}}^ 2\)
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
• Crystalline variational problems
• On Steiner’s Problem with Rectilinear Distance
• On the Steiner Problem
• Equilateral Sets in Minkowski Spaces
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