Integral Geometry and Geometric Probability

Table of Contents

Part I. Integral Geometry in the Plane:
1. Convex sets in the plane
2. Sets of points and Poisson processes in the plane
3. Sets of lines in the plane
4. Pairs of points and pairs of lines
5. Sets of strips in the plane
6. The group of motions in the plane: kinematic density
7. Fundamental formulas of Poincaré and Blaschke
8. Lattices of figures
Part II. General Integral Geometry:
9. Differential forms and Lie groups
10. Density and measure in homogenous spaces
11. The affine groups
12. The group of motions in En
Part III. Integral Geometry in En:
13. Convex sets in En
14. Linear subspaces, convex sets and compact manifolds
15. The kinematic density in En
16. Geometric and statistical applications: stereology
Part IV. Integral Geometry in Spaces of Constant Curvature:
17. Noneuclidean integral geometry
18. Crofton's formulas and the kinematic fundamental formula in noneuclidean spaces
19. Integral geometry and foliated spaces: trends in integral geometry.

Look Inside

• Table of Contents (209 KB)
• Front Matter (625 KB)
• Index (530 KB)
• Copyright Information Page (74 KB)
• Marketing Excerpt (445 KB)