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Geometric Tomography
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  • Cited by 146
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Gardner, Richard J. Hug, Daniel Weil, Wolfgang Xing, Sudan and Ye, Deping 2019. General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem I. Calculus of Variations and Partial Differential Equations, Vol. 58, Issue. 1,

    Zhao, Chang-Jian 2018. Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes. Journal of Function Spaces, Vol. 2018, Issue. , p. 1.

    Lutwak, Erwin Yang, Deane and Zhang, Gaoyong 2018. L p dual curvature measures. Advances in Mathematics, Vol. 329, Issue. , p. 85.

    Chen, Bin and Wang, Weidong 2018. Some inequalities for Lp radial Blaschke-Minkowski homomorphisms. Quaestiones Mathematicae, p. 1.

    张, 蕊 2018. The i th L<sub>p</sub> Dual Affine Surface Area. Pure Mathematics, Vol. 08, Issue. 01, p. 99.

    Zhang, Rui and Ma, Tongyi 2018. Generalized Intersection Bodies with Parameter. Wuhan University Journal of Natural Sciences, Vol. 23, Issue. 4, p. 301.

    Li, Tian and Wang, Weidong 2018. Some inequalities for asymmetric Lp-mean zonoids. Quaestiones Mathematicae, p. 1.

    Chen, Bin and Wang, Weidong 2018. Some inequalities for (p,q)$(p,q)$-mixed volume. Journal of Inequalities and Applications, Vol. 2018, Issue. 1,

    Ferrarello, Daniela Mammana, Maria Flavia and Pennisi, Mario 2018. Magic of centroids. International Journal of Mathematical Education in Science and Technology, Vol. 49, Issue. 4, p. 628.

    Chen, Bin and Wang, Weidong 2018. A Type of Busemann-Petty Problems for Blaschke-Minkowski Homomorphisms. Wuhan University Journal of Natural Sciences, Vol. 23, Issue. 4, p. 289.

    Li, Hai Lin, Youjiang and Wang, Weidong 2018. The $$({\varvec{q}},\varvec{\phi })$$(q,ϕ)-Dual Orlicz Mixed Affine Surface Areas. Results in Mathematics, Vol. 73, Issue. 4,

    Ryabogin, Dmitry 2018. Discrete Geometry and Symmetry. Vol. 234, Issue. , p. 297.

    Abardia-Evéquoz, J. Hernández Cifre, M. A. and Saorín Gómez, E. 2018. Mean projection and section radii of convex bodies. Acta Mathematica Hungarica, Vol. 155, Issue. 1, p. 89.

    Grinberg, Eric L. 2018. Comparing volumes by concurrent cross-sections of complex lines: a Busemann–Petty type problem. Positivity, Vol. 22, Issue. 5, p. 1297.

    Hou, S. and Xiao, J. 2018. A Mixed Volumetry for the Anisotropic Logarithmic Potential. The Journal of Geometric Analysis, Vol. 28, Issue. 3, p. 2028.

    Feng, Yibin and He, Binwu 2018. The (p, q)-mixed geominimal surface areas. Quaestiones Mathematicae, p. 1.

    Bezdek, Károly and Khan, Muhammad A. 2018. Discrete Geometry and Symmetry. Vol. 234, Issue. , p. 1.

    O'Hara, Jun 2018. Characterization of balls by generalized Riesz energy. Mathematische Nachrichten,

    Yaskin, Vladyslav 2018. An Extension of Polynomial Integrability to Dual Quermassintegrals. International Mathematics Research Notices,

    Vincze, Csaba 2018. On the taxicab distance sum function and its applications in discrete tomography. Periodica Mathematica Hungarica,

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Book description

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although primarily meant for researchers and graduate students in geometry and tomography, brief introductions, suitable for advanced undergraduates, are provided to the basic concepts. More than 70 illustrations are used to clarify the text. The book also presents 66 unsolved problems. Each chapter ends with extensive notes, historical remarks, and some biographies. This edition includes numerous updates and improvements, with some 300 new references bringing the total to over 800.

Reviews

praise for the first edition …‘The work is written in a very clear style, is well organized, and is amply provided with helpful illustrations and diagrams.’

Wm. J. Firey Source: SIAM Review

‘This is an extremely useful monograph, collecting together all the currently available material on geometric tomography … The book is well organized and easy to read, with many illustrations, and copious notes to each chapter … I recommend the book highly as a valuable introduction and continuing reference.’

Peter McMullen Source: Bulletin of the London Mathematical Society

‘… A valuable reference source. Libraries should have this book.’

A. G. Ramm Source: Inverse Problems Newsletter

‘This well-written book describes the recent theory … it includes copious notes and a comprehensive bibliography.’

Source: Mathematika

‘The book is self contained, readable and can be warmly recommended not only for specialists.’

Source: European Mathematical Society Newsletter

'… this book is a must for all those who are or plan to work on geometric tomography …'

Source: Acta Scientiarum Mathematicarum

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