Lluís Santaló

Abstract: 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 Poincare 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.

TL;DR: In this paper, a principal object is to study diagrames relacionat amb la representacio dels cossos convexos de l'espai com a punts del pla a partir dels seus tres elements fonamentals: volum V, area F i curvatura mitjana total M.