Monge patch
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In the differential geometry of surfaces, the Monge patch designates the parameterization of a surface by its height over a flat reference plane. It is also called Monge parameterization or Monge form. In physical theory of surface and interface roughness, and especially in the study of shape conformations of membranes, it is usually called the Monge gauge, or less frequently the Monge representation.
In the differential geometry of surfaces, the Monge patch designates the parameterization of a surface by its height over a flat reference plane. It is also called Monge parameterization or Monge form. In physical theory of surface and interface roughness, and especially in the study of shape conformations of membranes, it is usually called the Monge gauge, or less frequently the Monge representation. If the reference plane is the Cartesian xy plane, then in the Monge gauge the surface under study is fully characterized by its height z=u(x,y). Typically, the reference plane represents the average surface so that the first moment of the height is zero, =0. The Monge gauge has two obvious limitations: If the average surface is not plane, then the Monge gauge only makes sense on length scales smaller than the curvature of the average surface. And the Monge gauge fails completely if the surface is so strongly bent that there are overhangs (points x,y corresponding to more than one z).
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