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Zbl 0812.49032
Almgren, Fred
Questions and answers about area-minimizing surfaces and geometric measure theory. (English)
[A] Greene, Robert (ed.) et al., Differential geometry. Part 1: Partial differential equations on manifolds. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 1, 29-53 (1993). ISBN 0-8218-1494-X/hbk/pt.1; ISBN 0-8218-1493-1/set

The author offers ``informal personal answers'' to 40 questions ``which are sometimes asked about area minimization or geometric measure theory''. Examples are: What is an area-minimizing surface? What difference does the definition of area make? What kinds of area- minimizing surfaces can be computed? Have minimal surface computations been useful outside mathematics? Why are least area problems hard theoretically? What are the main successes of modern geometric measure theory? What are currents, why are they called that, and where did they come from? What are some of the main theorems about integral currents? What is the uniqueness of tangent cones problem? What are multifunctions and what are they good for? What are that chains mod $\nu$? What are crystalline minimal surfaces? What are calibrations? There are 80 references.
[M.Brokate (Kaiserslautern)]

MSC 2000:: *49Q20 Variational problems in geometric measure-theoretic setting
28A75 Geometric measure theory
32C30 Integration on analytic sets and spaces
52A27 Approximation by convex sets
74A55 Theories of friction (tribology)
74M15 Contact
53A10 Minimal surfaces, surfaces with prescribed mean curvature
65D18 Computer graphics and computational geometry

Keywords: geometric measure theory; area-minimizing surfaces; integral currents; tangent cones; multifunctions; crystalline minimal surfaces; calibrations

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