Pacific Journal of Mathematics

Decomposition of plane convex sets. I.

Ruth Silverman

Article information

Pacific J. Math., Volume 47, Number 2 (1973), 521-530.

First available in Project Euclid: 13 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52A10: Convex sets in 2 dimensions (including convex curves) [See also 53A04]


Silverman, Ruth. Decomposition of plane convex sets. I. Pacific J. Math. 47 (1973), no. 2, 521--530.

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  • [2] W. Fenchel, Convex Cones, Sets, and Functions,Princeton University, Princeton, 1953.
  • [3] Wm. J. Firey and B. Grnbaum, Addition and decomposition of convex polytopes, Israel J. Math., 2 No. 2, (1964).
  • [4] D. Gale, Irreducible convex sets, Proc. Intern. Congr. Math., Amsterdam, 2 (1954), 217-218.
  • [5] B. Grnbaum, Convex Polytopes, John Wiley and Sons, London, 1967.
  • [6] L. A. Lyusternik, Convex Figures and Polyhedra, translated by D. L. Barnett, C. Heath and Company, Boston, 1966.
  • [7] W. Meyer, Minkowski Addition of Convex Sets, University of Wisconsin, 1969. (Unpublished Ph. D. thesis).
  • [8] G. C. Shephard, Decomposable convex polyhedra, Mathematika 10, (1963), 89-95.
  • [9] I. M. Yaglom and V. G. Boltyanskii, Convex Figures, Moscow, 1951. Englishtransla- tion by P. J. Kelly and L. F. Walton. Holt, Rinehart and Winston, New York, 1961.

See also

  • II : Ruth Silverman. Decomposition of plane convex sets. II. Sets associated with a width function. Pacific Journal of Mathematics volume 48, issue 2, (1973), pp. 497-502.