The cut locus of an ellipsoid (Q1373246)

The cut locus of a connected compact set \(S\subset E^3\) with inner points is the closure of the set of points having more than one nearest point on the boundary of \(S\). Referring only to inner points of \(S\), the author proves that the cut locus of a general ellipsoid (with three different lengths of its main axes) is a region contained in that symmetry plane which is spanned by the two longer main axes.