Polar Height Function:

A height function is called polar if it has the minimum possible number of critical points.

For height functions on compact surfaces, this means the the height function has exactly one maximum and one minimum, and X(M) - 2 saddles, where X(M) is the Euler characteristic of the surface.

Polar height functions play an important role in describing tight immersions of surfaces in space. [More]

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8/12/94 dpvc@geom.umn.edu -- The Geometry Center