Integral Geometry and Valuations

• Main Authors: Alesker, Semyon (Author), Fu, Joseph H.G (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Gallego, Eduardo (Editor), Solanes, Gil (Editor)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
• Series: Advanced Courses in Mathematics - CRM Barcelona,
• Subjects: Mathematics.; Convex geometry.; Discrete geometry.; Differential geometry.; Convex and Discrete Geometry.; Differential Geometry.

Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to im...

Table of Contents:

• Part I: New Structures on Valuations and Applications
• Translation invariant valuations on convex sets
• Valuations on manifolds
• Part II: Algebraic Integral Geometry
• Classical integral geometry
• Curvature measures and the normal cycle
• Integral geometry of euclidean spaces via Alesker theory
• Valuations and integral geometry on isotropic manifolds
• Hermitian integral geometry.