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The 4-vertex theorem for convex curves R{sup 3}

Technical Report:

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.
Authors:
Publication Date:
Sep 01, 1991
Product Type:
Technical Report
Report Number:
IC-91/273
Reference Number:
SCA: 661100; PA: AIX-23:015326; SN: 92000647055
Resource Relation:
Other Information: PBD: Sep 1991
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EUCLIDEAN SPACE; VERTEX FUNCTIONS; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10113309
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE92615218; TRN: XA9130266015326
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
7 p.
Announcement Date:
Jun 30, 2005

Technical Report:

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}
}