The 4-vertex 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:
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- Curves (Geometry);
- Euclidean Geometry;
- Functions (Mathematics);
- Quantum Theory;
- Convexity;
- Extremum Values;
- Theorems;
- Thermodynamics and Statistical Physics