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Embedded Surface


A surface S is n-embeddable if it can be placed in R^n-space without self-intersections, but cannot be similarly placed in any R^k for k<n. A surface so embedded is said to be an embedded surface. The Costa minimal surface and gyroid are embeddable in R^3, but the Klein bottle is not (the commonly depicted R^3 representation requires the surface to pass through itself).

There is particular interest in surfaces which are minimal, complete, and embedded.


See also

Costa Minimal Surface, Embeddable Knot, Gyroid, Minimal Surface

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References

Collin, P. "Topologie et courbure des surfaces minimales proprement plongées de R^3." Ann. Math. 145, 1-31, 1997.Hoffman, D. and Karcher, H. "Complete Embedded Minimal Surfaces of Finite Total Curvature." In Minimal Surfaces (Ed. R. Osserman). Berlin: Springer-Verlag, pp. 267-272, 1997.Nikolaos, K. "Complete Embedded Minimal Surfaces of Finite Total Curvature." J. Diff. Geom. 47, 96-169, 1997.Pérez, J. and Ros, A. "The Space of Properly Embedded Minimal Surfaces with Finite Total Curvature." Indiana Univ. Math. J. 45, 177-204, 1996.Ros, A. "Compactness of Spaces of Properly Embedded Minimal Surfaces with Finite Total Curvature." Indiana Univ. Math. J. 44, 139-152, 1995.

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Embedded Surface

Cite this as:

Weisstein, Eric W. "Embedded Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EmbeddedSurface.html

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