Back
 OJDM  Vol.7 No.2 , April 2017
Boundaries of Smooth Strictly Convex Sets in the Euclidean Plane R2
Show more
Abstract: We give a characterization of the boundaries of smooth strictly convex sets in the Euclidean plane Rbased on the existence and uniqueness of inscribed triangles.
Cite this paper: Kramer, H. (2017) Boundaries of Smooth Strictly Convex Sets in the Euclidean Plane R2. Open Journal of Discrete Mathematics, 7, 71-76. doi: 10.4236/ojdm.2017.72008.
References

[1]   Blaschke, W. (1916) Kreis und Kugel. Verlag von Veit & Comp, Leipzig.

[2]   Boltyanski, V., Martini, H. and Soltan, P.S. (1997) Excursion into Combinatorial Geometry. Springer-Verlag, Heidelberg.
https://doi.org/10.1007/978-3-642-59237-9

[3]   Bonnesen, T. and Fenchel, W. (1974) Theorie der konvexen Körper. Springer-Ver-lag, Heidelberg.
https://doi.org/10.1007/978-3-642-93014-0

[4]   Valentine, F.A. (1968) Konvexe Mengen. Hochschultaschenbücher-Verlag, Mannheim.

[5]   Webster, R. (1994) Convexity. Oxford University Press, Oxford.

[6]   Menger, K. (1931) Some Applications of Point Set Methods. Annals of Mathematics, 32, 739-750.
https://doi.org/10.2307/1968317

[7]   Juul, K. (1975) Some Three-Point Subset Properties Connected with Menger’s Characterization of Boundaries of Plane Convex Sets. Pacific Journal of Mathematics, 58, 511-515.
https://doi.org/10.2140/pjm.1975.58.511

[8]   Mani-Levitska, P. (1993) Characterization of Convex Sets. In: Gruber, P.M. and Wills, J.M., Eds., Handbook of Convex Geometry, North-Holland, 19-41.

[9]   Kramer, H. (1978) A Characterization of Boundaries of Smooth Strictly Convex Plane Sets. Revue d’analyse numérique et de théorie de l'approximation, 7, 61-65.

[10]   Kramer, H. (1979) Boundaries of Smooth Strictly Convex Plane Sets. Revue d’analyse numérique et de théorie de l'approximation, 8, 59-66.

[11]   Kramer, H. and Németh, A.B. (1972) Triangles Inscribed in Smooth Closed Arcs. Revue d’analyse numérique et de théorie de l'approximation, 1, 63-71.

[12]   Caratheodory, C. (1911) Ueber den Variabilitaetsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen. Rendiconti del Circolo Matematico di Palermo, 32, 193-217.
https://doi.org/10.1007/BF03014795

 
 
Top