The product on smooth and generalized valuations
By Semyon Alesker, A. Bernig. 2009
54 citations recorded by the source corpus.
The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms, and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to transversal intersections. This result is used to prove a general kinematic formula on compact rank one symmetric spaces.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3eb13c337d07d3c5f033213fd72a29717046348f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- A. Bernig
- Judit Abardia
- Daniel Hug
- Joseph H. G. Fu
- G. Solanes
- Thomas Wannerer
- Franz E. Schuster
- Semyon Alesker
In Mathematical Physics
- Joseph H. G. Fu
- G. Solanes
- Daniel Hug
- Judit Abardia
- A. Bernig
- Thomas Wannerer
- Franz E. Schuster
- Christoph Haberl
Citations in the corpus
- Kinematic formulas for tensor valuations (2014, methodology): “We refer to [36] for the basic properties of D and to [12, 14, 16] for applications in integral geometry, some of which will be explained in more detail below.”
- Integral geometry of complex space forms (2012, methodology): “The next theorem was shown in [18] and [11], assuming M to be flat or compact respectively.”
- Difference bodies in complex vector spaces (2012, background): “See [6, 8, 11] for more information on smooth valuations.”
- Algebraic Integral Geometry (2010, background): “o valuations and not to curvature measures. (2) We have described in detail the theory of valuations on an affine space. The theory of valuations on manifolds was recently worked out, mainly by Alesker [11, 12, 18, 14, 13, 24, 23, 16]. This gives the appropriate framework to study integral geometry of”