## Patch

A patch (also called a Local Surface) is a differentiable mapping , where is an open subset of . More generally, if is any Subset of , then a map is a patch provided that can be extended to a differentiable map from into , where is an open set containing . Here, (or more generally, ) is called the Trace of x.

See also Gauss Map, Injective Patch, Monge Patch, Regular Patch, Trace (Map)

References

Gray, A. Patches in .'' §10.2 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 183-184 and 192-193, 1993.