Minimum problems for volumes of convex bodies

Partial Differential Equations and Applications: Collected Papers in Honor of Carlo Pucci

Volumn , Issue , 2017, Pages 43-55

  Campi, Stefano ^a   Colesanti, Andrea ^b   Gronchi, Paolo ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

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[No Author keywords available]

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EID: 84964677011     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9780203744369     Document Type: Chapter

References (30)

1. Besicovitch, A. S. (1963), Minimum area of a set of constant width, Proc. of Symposia in Pure Math. Vol. 7, Convexity, Amer. Math. Soc, 13-4.
2. Blaschke, W. (1915), Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts, Math. Annalen 76, 504-13.
3. Blaschke, W. (1916), Kreis und Kugel, (Veit, Leipzig), 2nd Ed. W. de Gruyter, Berlin, 1956.
4. Bonnesen, T., Fenchel, W. (1934), Theorie der konvexen Körper, Springer, Berlin.
5. Chakerian, G. D. (1966), Sets of constant width, Pacific J. Math. 19,1, 13-21.
6. Chakerian, G. D., Groemer, H. (1983), Convex bodies of constant width, Convexity and its applications (P. Gruber, J. M. Wills, eds.), Birkhäuser, Basel, pp. 49-96.
7. Eggleston, H. G. (1952), A proof of Blaschkefs theorem on the Reuleaux triangle, Quart. J. Math. Oxford Ser. 2, 3, 296-7.
8. Evans, L. C., Gariepy, R. F. (1992), Measure theory and fine properties of functions, CRC press, Boca Raton.
9. Firey, W. J. (1965), The brightness of convex bodies, Tech. Report 19, Oregon State Univ., Corvallis, Oregon.
10. Fujiwara, M. (1927, 1931), Analytical proof of Blaschke’s theorem on the curve of constant breadth with minimum area, I and II, Proc. Imp. Acad. Japan 3 (1927), 7 (1931), 307-9 (1927), 300-2 (1931).
11. Gardner R. J. (1995), Geometric tomography, Cambridge University Press, New York.
12. Goodey, P., Weil, W. (1993), Zonoids and generalizations, Handbook of convex geometry (P. Gruber, J. M. Wills, eds.), North-Holland, Amsterdam, pp. 1297-326.
13. Gruber, P., Schneider, R. (1979), Problems in geometric convexity, Contributions to geometry (J. Tölke, J. M. Wills, eds.), Birkhäuser, Berlin, pp. 255-78.
14. Hadwiger, H. (1949), Elementare Studie über konvexe Körper, Math. Nachr. 2, 114-23.
15. Heil, E. (1978), Kleinste konvexe Körper gegebener Dicke, Preprint no. 453, Technische Hochschule Darmstadt.
16. Heil, E., Martini, H. (1993), Special convex bodies, Handbook of convex geometry (P. Gruber, J. M. Wills, eds.), North-Holland, Amsterdam, pp. 347-85.
17. Hilbert, D., Cohn-Vossen, S. (1932), Anschauliche Geometrie, Springer, Berlin.
18. Kallay, M. (1974), Reconstruction of a plane convex body from the curvature of its boundary, Israel J. Math. 17, 149-61.
19. Lebesgue, H. (1914), Sur le problème des isopérimètres et sur le domaines de largeur constante, Bull. Soc. Math. Franc., C.R., 72-76.
20. Mayer, A. E. (1934-35), Der Inhalt der Gleichdicke, Math. Annalen 110, 97-127.
21. Martini, H. (1994), Cross-sectional measures, Colloquia Mathematica Societatis János Bolyai, vol. 63, Intuitive Geometry, North-Holland, Amsterdam, pp. 269-310.
22. Meissner, E. (1912), Drei Gipsmodelle von Flächen konstanter Breite, Z. Math. Phys. 60, 92-4.
23. Pál, J. (1921), Ein Minimumproblem für Ovale, Math. Annalen 83, 311-9.
24. Petty, C. M. (1967), Projection bodies, Proc. Colloquium Convexity, Copenhagen, 1965, Københavns Univ. Math. Inst., pp. 234-41.
25. Rogers, C. A., Shephard G. C. (1957), The difference body of a convex body, Arch. Math. 8, 220-33.
26. Schneider, R. (1967), Zu einem Problem von Shephard über die Projektionen konvexer Körper, Math. Zeitschr. 101, 71-82.
27. Schneider, R. (1993), Convex bodies: the Brunn-Minkowski theory, Cambridge University Press, Cambridge.
28. Schramm, O. (1988), On the volume of sets having constant width, Israel J. Math. 63, 2, 178-82.
29. Sholander, M. (1952), On certain minimum problems in the theory of convex curves, Trans. Amer. Math. Soc. 73, 139-73.
30. Zhang, G. (1991), Restricted chord projection and affine inequalities, Geom. Dedicata 39, 213-22.