The 4vertex theorem for convex curves R(sup 3)
Abstract
It is a well known fact that any smooth closed plane curve with nowhere vanishing curvature has at least four vertices (local extremum points of its curvature). A generalization of this statement for the case of space curves is known as a conjecture of P. Scherk. Here we sketch the proof of this conjecture.
 Publication:

Unknown
 Pub Date:
 September 1991
 Bibcode:
 1991vtcc.rept.....S
 Keywords:

 Curves (Geometry);
 Euclidean Geometry;
 Functions (Mathematics);
 Quantum Theory;
 Convexity;
 Extremum Values;
 Theorems;
 Thermodynamics and Statistical Physics