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.

* 8/12/94 dpvc@geom.umn.edu -- *

*The Geometry Center*