TOPICS
A surface 
is 
-embeddable if it can be placed in 
-space without self-intersections, but cannot be similarly
placed in any 
for 
.
A surface so embedded is said to be an embedded surface. The Costa
minimal surface and gyroid are embeddable in 
, but the Klein
bottle is not (the commonly depicted 
representation requires the surface to pass through itself).
There is particular interest in surfaces which are minimal, complete, and embedded.
." 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.Weisstein, Eric W. "Embedded Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EmbeddedSurface.html