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)
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.