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. (author). 5 refs.
Citation Formats
Sedykh, V D.
The 4-vertex theorem for convex curves R{sup 3}.
IAEA: N. p.,
1991.
Web.
Sedykh, V D.
The 4-vertex theorem for convex curves R{sup 3}.
IAEA.
Sedykh, V D.
1991.
"The 4-vertex theorem for convex curves R{sup 3}."
IAEA.
@misc{etde_10113309,
title = {The 4-vertex theorem for convex curves R{sup 3}}
author = {Sedykh, V D}
abstractNote = {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. (author). 5 refs.}
place = {IAEA}
year = {1991}
month = {Sep}
}
title = {The 4-vertex theorem for convex curves R{sup 3}}
author = {Sedykh, V D}
abstractNote = {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. (author). 5 refs.}
place = {IAEA}
year = {1991}
month = {Sep}
}