Hard Lefschetz Theorem for Valuations, Complex Integral Geometry, and Unitarily Invariant Valuations
نویسندگان
چکیده
منابع مشابه
Lefschetz theorem for valuations , complex integral geometry , and unitarily invariant valuations
We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of unitarily invariant translation invariant continuous valuations. It implies new integral geometric formulas for real submanifolds in Hermitian spaces genera...
متن کاملSe p 20 02 Hard Lefschetz theorem for valuations , complex integral geometry , and unitarily invariant
We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of unitarily invariant translation invariant continuous valuations. It implies new integral geometric formulas for real submanifolds in Hermitian spaces genera...
متن کاملLefschetz theorem for valuations and related questions of integral geometry
We continue studying the properties of the multiplicative structure on valuations. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss problems of integral geometry staying behind these properties. Then we formulate a conjectural analogue of this result for odd valuations.
متن کاملIntegral Geometry of Tensor Valuations
We prove a complete set of integral geometric formulas of Crofton type (involving integrations over affine Grassmannians) for the Minkowski tensors of convex bodies. Minkowski tensors are the natural tensor valued valuations generalizing the intrinsic volumes (or Minkowski functionals) of convex bodies. By Hadwiger’s general integral geometric theorem, the Crofton formulas yield also kinematic ...
متن کاملAn Integral Geometric Theorem for Simple Valuations
We prove a translative mean value formula for simple valuations, taken at the intersection of a fixed and a translated convex body. MSC 2000: 52A22 (primary); 52B45 (secondary)
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2003
ISSN: 0022-040X
DOI: 10.4310/jdg/1080835658