Valuations on Manifolds and Integral Geometry

Semyon Alesker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We construct new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon-type transform on valuations is introduced using these operations and the product on valuations. It is shown that the classical Radon transform on smooth functions, and the well-known Radon transform on constructible functions, with respect to the Euler characteristic, are special cases of this new Radon transform. An inversion formula for the Radon transform on valuations has been proven in a specific case of real projective spaces. Relations of these operations to yet another classical type of integral geometry, Crofton and kinematic formulas, are indicated.

Original languageEnglish
Pages (from-to)1073-1143
Number of pages71
JournalGeometric and Functional Analysis
Volume20
Issue number5
DOIs
StatePublished - Nov 2010

Funding

FundersFunder number
Israel Science Foundation701/08

    Keywords

    • Radon transform
    • Valuations
    • manifolds

    Fingerprint

    Dive into the research topics of 'Valuations on Manifolds and Integral Geometry'. Together they form a unique fingerprint.

    Cite this