Richard Gardner has been Professor of Mathematics at Western Washington University since 1991. He is the author of 70 papers and founded geometric tomography as a subject in its own right with the publication of the first edition of this book in 1995.
Inhaltsangabe
Preface to the second edition Preface 0. Background material 1. Parallel X-rays of planar convex bodies 2. Parallel X-rays in n dimensions 3. Projections and projection functions 4. Projection bodies and volume inequalities 5. Point X-rays 6. Chord functions and equichordal problems 7. Sections, section functions, and point X-rays 8. Intersection bodies and volume inequalities 9. Estimates from projection and section functions Appendix A. Mixed volumes and dual mixed volumes Appendix B. Inequalities Appendix C. Integral transforms References Notation Author index Subject index.
0. Background material; 1. Parallel X-rays of planar convex bodies; 2. Parallel X-rays in n dimensions; 3. Projections and projection functions; 4. Projection bodies and volume inequalities; 5. Point X-rays; 6. Chord functions and equichordal problems; 7. Sections, section functions, and point X-rays; 8. Intersection bodies and volume inequalities; 9. Estimates from projection and section functions; A. Mixed volumes and dual mixed volumes; B. Inequalities; C. Integral transforms.
Preface to the second edition Preface 0. Background material 1. Parallel X-rays of planar convex bodies 2. Parallel X-rays in n dimensions 3. Projections and projection functions 4. Projection bodies and volume inequalities 5. Point X-rays 6. Chord functions and equichordal problems 7. Sections, section functions, and point X-rays 8. Intersection bodies and volume inequalities 9. Estimates from projection and section functions Appendix A. Mixed volumes and dual mixed volumes Appendix B. Inequalities Appendix C. Integral transforms References Notation Author index Subject index.
0. Background material; 1. Parallel X-rays of planar convex bodies; 2. Parallel X-rays in n dimensions; 3. Projections and projection functions; 4. Projection bodies and volume inequalities; 5. Point X-rays; 6. Chord functions and equichordal problems; 7. Sections, section functions, and point X-rays; 8. Intersection bodies and volume inequalities; 9. Estimates from projection and section functions; A. Mixed volumes and dual mixed volumes; B. Inequalities; C. Integral transforms.
Rezensionen
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, SIAM Review
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