Even valuations on convex bodies

Transactions of the American Mathematical Society

Volumn 352, Issue 1, 2000, Pages 71-93

  Klain, Daniel A ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844456159     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02240-0     Document Type: Article

References (36)

1. W. Blaschke. Kreis und Kugel, Leipzig, 1916.
2. V. Boltianskii. Hilbert's Third Problem. (New York: John Wiley fe Sons, 1978). MR 58:18074
3. G. D. Chakerian and E. Lutwak. Bodies with similar projections, Trans. Amer. Math. Soc., 349 (1997), 1811-1820. MR 98a:52011
4. M. Dehn. Über den Rauminhalt, Math. Ann., 55 (1901), 465-478.
5. R. Gardner. Geometrie Tomography (New York: Cambridge University Press, 1995). MR 96J-.52006
6. P. Goodey and R. Howard. Processes of flats induced by higher dimensional processes, Adv. Math., 80 (1990), 92-109. MR 91d:60025
7. P. Goodey, R. Schneider, and W. Weil. Projection functions on higher rank Grassmannians, Geometric Aspects of Functional Analysis, 3. Lindenstrauss and V. D. Milman, Eds., Oper. Theory Adv. Appl., 77 (1995), 75-90. MR 96h:52007
8. P. Goodey, R. Schneider, and W. Weil. Projection functions of convex bodies. Intuitive Geometry (Budapest, 1995), Bolyai Soc. Math. Stud., 6 (1997), 23-53. MR 98k:52020
9. P. Goodey and W. Weil. Distributions and valuations, Proc. London Math. Soc., Series 3, 49 (1984), 504-516. MR 86f:52008
10. P. Goodey and W. Weil. Zonoids and generalisations, Handbook of Convex Geometry, Peter M. Gruber and Jörg M. Wills, Eds. (Amsterdam: North-Holland, 1993), 1297-1326. MR 95g:52015
11. E. Grinberg. Radon transforms on higher rank Grassmannians, J. Differential Geom., 24 (1986), 53-68. MR 87m:22023
12. E. Grinberg. Cosine and Radon transforms on Grassmannians. Preprint.
13. E. Grinberg and G. Zhang. Convolutions, transforms and convex bodies, Proc. London Math. Soc. (3), 78 (1999), 77-115.
14. H. Groemer. On the extension of additive functionals on classes of convex sets, Pacific J. Math., 75 (1978), 397-410. MR 58:24003
15. H. Hadwiger. Altes und Neues über konvexe Körper. (Basel: Birkhäuser Verlag, 1955). MR 17:401e
16. H. Hadwiger. Vorlesungen über Inhalt, Oberfläche, und Isoperimetrie. (Berlin: Springer Verlag, 1957). MR 21:1561
17. H. Hadwiger and P. Glur. Zerlegungsgleichheit ebener Polygone, Elem. Math., 6 (1951), 97-106. MR 13:576k
18. D. Hubert. Mathematical Problems. Lecture delivered before the International Congress of Mathematicians in Paris, 1900. Translated by M. W. Newson, Bull. Amer. Math. Soc., 8 (1902), 437-479.
19. L. Hörmander. The Analysis of Linear Partial Differential Operators I, 2nd edition. (New York: Springer-Verlag, 1990). MR 91m:35001b
20. D. Klain. A short proof of Hadwiger's characterization theorem, Mathematika, 42 (1995), 329-339. MR 97e:52008
21. D. Klain and G.-C. Rota. Introduction to Geometric Probability. (New York: Cambridge University Press, 1997. CMP 98:09
22. E. Lutwak. Extended affine surface area, Adv. Math., 85 (1991), 39-68. MR 92d:52012
23. P. McMullen. Non-linear angle-sum relations for polyhedral cones and polytopes, Math. Proc. Camb. Phil. Soc., 78 (1975), 247-261. MR 52:15238
24. P. McMullen. Valuations and Euler-type relations on certain classes of convex polytopes, Proc. London Math. Soc., 35 (1977), 113-135. MR 56:6548
25. P. McMullen. Continuous translation invariant valuations on the space of compact convex sets, Arch. Math., 34 (1980), 377-384. MR 81m:52013
26. P. McMullen. Valuations and dissections, Handbook of Convex Geometry, Peter M. Gruber and Jörg M. Wills, Eds. (Amsterdam: North-Holland, 1993), 933-988. MR 95f:52018
27. P. McMullen and R. Schneider. Valuations on convex bodies, Convexity and Its Applications, Peter M. Gruber and Jörg M. Wills, Eds. (Boston: Birkhäuser Verlag, 1983), 170-247. MR 85e:52001
28. I. Richards and H. Youn. Theory of Distributions: a non-technical introduction. (New York: Cambridge University Press, 1990). MR 91f:46003
29. C.-H. Sah. Hubert's Third Problem: Scissors Congruence. (San Francisco: Fearon Pitman Publishers Inc., 1979). MR 81g:51011
30. R. Schneider. Equivariant cndomorphisms of the space of convex bodies, Trans. Amer. Math. Soc., 194 (1974), 53-78. MR 50:5633
31. R. Schneider. Convex Bodies: The Brunn-Minkowski Theory. (New York: Cambridge University Press, 1993). MR 94d:52007
32. R. Schneider. Simple valuations on convex bodies, Mathematika, 43 (1996), 32-39. MR 97f:52016
33. W. Weil. Kontinuierliche Linearkombination von Strecken, Math. Z., 148 (1976), 71-84. MR 53:3887
34. W. Weil. Centrally symmetric convex bodies and distributions, Israel J. Math., 24 (1976), 352-367. MR 54:8450
35. W. Weil. Centrally symmetric convex bodies and distributions II, Israel J. Math., 32 (1979), 173-182. MR 80g:52003
36. W. Weil. Stereology: A survey for geometers, Convexity and Its Applications, Peter M. Gruber and Jörg M. Wills, Eds. (Boston: Birkhäuser Verlag, 1983). MR 85e:52007