A representation for the generating density of convex bodies

Lobachevskii Journal of Mathematics - Tập 30 - Trang 97-100 - 2009
R. H. Aramyan1
1Institute of Mathematics, Armenian Academy of Sciences, Yerevan, Armenia

Tóm tắt

We get a new representation for the generating density of convex bodies in R 3 in terms of curvature radii of their projections, which is dual to the classical representation of W. Blaschke.

Tài liệu tham khảo

R. V. Ambartzumian, Combinatorial integral geometry, metric and zonoids, Acta Appl.Math. 9, 3 (1987). R. H. Aramyan, Curvature radii of planar projections of convex bodies in Rn [in Russian], Izv. Akad. Nauk Armenii. Matematika [English translation: Journal of Contemporary Math. Anal. (Armenian Academy of Sciences)] 37(1), 2 (2002). R. H. Aramyan, An approach to generalized Funk equations, I [in Russian], Izv. Akad. Nauk Armenii. Matematika [English translation: Journal of Contemporary Math. Anal. (Armenian Academy of Sciences)] 36(1), 47 (2001). R. H. Aramyan, Generalized Radon transform with an application in convexity theory, I [in Russian], Izv. Akad. Nauk Armenii. Matematika [English translation: Journal of Contemporary Math. Anal. (Armenian Academy of Sciences)] 38(3), 16 (2003). W. Blaschke, Kreis und Kugel (Veit, Leipzig), 2nd Ed. De Gruyter (Berlin, 1956). W. Wiel, R. Schneider, Zonoids and related Topics, in Convexity and its Applications, Ed. P. Gruber and J. Wills (Birkhauser, Basel, 1983).