The classical theory of minimal surfaces

By W. H. Meeks, Joaquín Pérez. 2011

105 citations recorded by the source corpus.

We present here a survey of recent spectacular successes in classical minimal surface theory. We highlight this article with the theorem that the plane, the helicoid, the catenoid and the one-parameter family fRtgt2(0;1) of Riemann minimal examples are the only complete, properly embedded, minimal planar domains in R 3 ; the proof of this result depends primarily on work of Colding

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4c1f1c3176b0c39157248d56bdd0847207514801

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1. Yunfei Zhang
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3. Lorenzo Valdevit
4. B. Endo
5. J. Bauer

Citations in the corpus

• The mechanical response of cellular materials with spinodal topologies (2019, background): “These topologies usually take the form of a locally area-minimized geometry (Meeks and Perez, 2011), and are characterized by a mean curvature approximately equal to zero everywhere on the surface.”