By Eric L Grinberg, Gaoyong Zhang, Jiazu Zhou
Indispensable geometry, often called geometric likelihood long ago, originated from Buffon's needle scan. extraordinary advances were made in numerous components that contain the speculation of convex our bodies. This quantity brings jointly contributions by way of major overseas researchers in vital geometry, convex geometry, complicated geometry, chance, information, and different convexity similar branches. The articles disguise either contemporary effects and fascinating instructions for destiny study.
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Extra resources for Integral Geometry And Convexity: Proceedings of the International Conference, Wuhan, China, 18 - 23 October 2004
Guy, Unsolved problems in geometry, Springer-Verlag, Berlin 1991. 6. H. G. Eggleston, The maximal length of chords bisecting the area or perimeter length of plane convex sets, Jour. London Math. Soc. 36 (1961), 122-128. 7. P. R. Goodey, A characterization of circles, Bull. London Math. Soc. 4 (1972), 199-201. 8. P. R. Goodey, Mean square inequalities for chords of convex sets, Israel Jour. Math. 42 (1982), 132-150. 9. Hans Herda, A conjectured characterization of circles, Amer. Math. Monthly 78 (1971), 888-889.
John, F. Plane Waves and Spherical Means Applied to Partial Differenial Equations, Dover Publications, New York, (2004). 14. , private communication. 15. , The Radon transform in spaces of matrices and in Grassmann manifolds, Dokl. Akad. Nauk SSSR, 177, No. 4 (1967), 1504-1507. 16. , Moscow, 15 (1970), 279-315 (Russian) . 17. Rouvire, F. Inverting Radon transforms: the group-theoretic approach, Enseign. Math. (2) 47 (2001), no. 3-4, 205-252. 18. Zhang, Genkai, Radon Transform on Real, Complex and Quatemionic Grassmannians, Preprint (2005).
Gelfand and collaborators introduced the Kappa Operator  and used it to study the Radon transform on fc-dimensional planes. Later they extended this notion to the study of Radon transforms for a pair of Grassmannians . The idea is to use the algebraic topology of Grassmann manifolds to exhibit inversion formulas as integrals of differential forms and to interpret the injectivity problem as a search for good homology cycles. For an introduction to this method and a variation of context see .
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