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The converse of the four vertex theorem
Author(s):
Björn
E. J.
Dahlberg
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2131-2135.
MSC (2000):
Primary 53A04
Posted:
January 31, 2005
MathSciNet review:
2137880
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Abstract:
We establish the converse to the four vertex theorem without the positivity condition.
References:
- 1.
- D. Fog, Über den Vierscheitelsatz und seine Verallgemeinerungen, Sitzungsbereiche der Berlin Akademie der Wissenschaft (1933), 251-254.
- 2.
- H. Gluck, The converse of the four vertex theorem, L'Enseignement Mathématique,
 Serie, Tome XVII (1971), 295-309. MR 0344998 (49:9737) - 3.
- S. B. Jackson, Vertices for plane curves, Bulletin of the American Mathematical Society 50 (1944), 564-578. MR 0010992 (6:100e)
- 4.
- S. Mukhopadhyaya, New methods in the geometry of a plane arc, Bull. Calcutta Math. Soc. 1 (1909), 31-37.
- 5.
- L. Vietoris, Ein einfacher Beweis des Vierscheitelsatzes der ebenen Kurven, Archiv der Mathematik 3 (1952), 97-102. MR 0052137 (14:577h)
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Additional Information:
Björn
E. J.
Dahlberg
Affiliation:
Department of Mathematics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
DOI:
10.1090/S0002-9939-05-07788-9
PII:
S 0002-9939(05)07788-9
Received by editor(s):
March 10, 2003
Received by editor(s) in revised form:
March 29, 2004
Posted:
January 31, 2005
Additional Notes:
The author was supported by a grant from the NFR, Sweden.
Björn Dahlberg died on the 30th of January 1998. The results of this paper appeared in his posthumous work. The final version was prepared by Vilhelm Adolfsson and Peter Kumlin, Department of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden; email: vilhelm@math.chalmers.se
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2005,
American Mathematical Society
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