A minimal surface is a surface that locally minimizes its area for a given boundary. More formally, a minimal surface is defined as a surface with a mean curvature of zero at every point. This means that, at each point on the surface, the surface is as flat as possible and does not bend upwards or downwards. Minimal surfaces can often be described using parametric equations or as graphs of functions.
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A minimal submanifold has vanishing mean curvature vector. For a surface in , this says that the scalar mean curvature is zero, equivalently that its two principal curvatures sum to zero.