Mathematische Zeitschrift

, Volume 173, Issue 2, pp 185–194

On the intermediate area functions of convex bodies

  • Paul R. Goodey
  • Rolf Schneider
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aleksandrov, A.D.: Zur Theorie der gemischten Volumina von konvexen Körpern I. Mat. Sb. (2)2, 947–972 (1937) [Russian]Google Scholar
  2. 2.
    Aleksandrov, A.D.: Zur Theorie der gemischten Volumina von konvexen Körpern II. Mat. Sb. (2)2, 1205–1238 (1937) [Russian]Google Scholar
  3. 3.
    Aleksandrov, A.D.: Zur Theorie der gemischten Volumina von konvexen Körpern III. Mat. Sb. (2)3, 27–46 (1938) [Russian]Google Scholar
  4. 4.
    Berg, Ch.: Corps convexes et potentiels sphériques. Danske Vid. Selsk. Mat.-Fys. Medd.37, 6 (1969)Google Scholar
  5. 5.
    Blaschke, W.: Kreis und Kugel. Leipzig: Veit 1916Google Scholar
  6. 6.
    Busemann, H.: Convex surfaces. New York: Interscience 1958Google Scholar
  7. 7.
    Chakerian, G.D.: Higher dimensional analogues of an isoperimetric inequality of Benson. Math. Nachr.48, 33–41 (1971)Google Scholar
  8. 8.
    Fenchel, W., Jessen, B.: Mengenfunktionen und konvexe Körper. Danske Vid. Selsk. Mat.-Fys. Medd.16, 3 (1938)Google Scholar
  9. 9.
    Firey, W.J.: The brightness of convex bodies. Technical Report no.19. Corvallis: Oregon State University 1965Google Scholar
  10. 10.
    Firey, W.J.: Blaschke sums of convex bodies and mixed bodies. Proceedings of the Colloquium on Convexity (Copenhagen 1965), pp 94–101. Københavns Universitets Matematiske Institut 1967Google Scholar
  11. 11.
    Firey, W.J.: Generalized convex bodies of revolution. Canad. J. Math.14, 972–996 (1967)Google Scholar
  12. 12.
    Firey, W.J.: Christoffel's problem for general convex bodies. Mathematika15, 7–21 (1968)Google Scholar
  13. 13.
    Firey, W.J.: Local behaviour of area functions of convex bodies. Pacific J. Math.35, 345–357 (1970)Google Scholar
  14. 14.
    Firey, W.J.: Intermediate Christoffel-Minkowski-problems for figures of revolution. Israel J. Math.8, 384–390 (1970)Google Scholar
  15. 15.
    Firey, W.J.: The determination of convex bodies by elementary symmetric functions of principal radii of curvature. Mimeographed manuscript 1970Google Scholar
  16. 16.
    Firey, W.J.: Some open questions on convex surfaces. In: Proceedings of the International Congress of Mathematicians (Vancouver 1974) pp. 479–484. Vancouver: Canadian Mathematical Congress 1975Google Scholar
  17. 17.
    Firey, W.J., Grünbaum, B.: Addition and decomposition of convex polytopes. Israel J. Math.2, 91–100 (1964)Google Scholar
  18. 18.
    Goikhman, D.M.: The differentiability of volume in Blaschke lattices. Sibirsk. Mat. Ž.15, 1406–1408 (1974) [Russian]. English translation: Siberian Math. J.15, 997–999 (1974)Google Scholar
  19. 19.
    Grünbaum, B.: Convex polytopes. London-New York-Sidney: Interscience 1967Google Scholar
  20. 20.
    Klee, V.L.: Some characterizations of convex polyhedra. Acta Math.102, 79–107 (1959)Google Scholar
  21. 21.
    Kneser, H., Süss, W.: Die Volumina in linearen Scharen konvexer Körper. Mat. Tidsskr. B, 19–25 (1932)Google Scholar
  22. 22.
    Kutateladze, S.S.: Blaschke structures in the programming of isoperimetric problems. Mat. Zametki14, 745–754 (1973) [Russian]. English translation: Math. Notes14, 985–989 (1973)Google Scholar
  23. 23.
    Kutateladze, S.S.: Symmetry measures. Mat. Zametki19, 615–622 (1976) [Russian]. English translation: Math. Notes19, 372–375 (1976)Google Scholar
  24. 24.
    Kutateladze, S.S., Rubinov, A.M.: Problems of isoperimetric type in a space of convex bodies. Optimal. Planirovanie14, 61–79 (1969) [Russian]Google Scholar
  25. 25.
    Minkowski, H.: Allgemeine Lehrsätze über die konvexen Polyeder. Nachr. Ges. Wiss. Göttingen, 198–219 (1897)Google Scholar
  26. 26.
    Schneider, R.: Kinematische Berührmaße für konvexe Körper und Integralrelationen für Oberflächenmaße. Math. Ann.218, 253–267 (1976)Google Scholar
  27. 27.
    Schneider, R.: Curvature measures of convex bodies. Ann. Mat. Pura Appl.116, 101–134 (1978)Google Scholar
  28. 28.
    Süss, W.: Zusammensetzung von Eikörpern und homothetische Eiflächen. Tôhoku Math. J.35, 47–50 (1932)Google Scholar
  29. 29.
    Weil, W.: Ein Approximationssatz für konvexe Körper. Manuscripta Math.8, 335–362 (1973)Google Scholar
  30. 30.
    Weil, W.: On surface area measures of convex bodies. Geometriae Dedicata (to appear)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Paul R. Goodey
    • 1
  • Rolf Schneider
    • 2
  1. 1.Mathematics DepartmentRoyal Holloway CollegeEnglefield GreenUK
  2. 2.Mathematisches Institut der UniversitätFreiburgFederal Republic of Germany

Personalised recommendations