@article{a9bfb17defc7467394e87cc17f52db55,
title = "Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry",
abstract = "The recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a K{\"u}nneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.",
keywords = "Curvature measure, Lipschitz–Killing measures, Pseudo-Riemannian manifolds, Valuation, Weyl principle",
author = "Andreas Bernig and Dmitry Faifman and Gil Solanes",
note = "Funding Information: A.B. was supported by DFG grant BE 2484/5-2 Funding Information: D.F. was partially supported by an NSERC Discovery Grant. Funding Information: G.S. was supported by FEDER/MICINN grant PGC2018-095998-B-I00 and the Serra H{\'u}nter Programme. Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
month = dec,
doi = "10.1007/s12220-021-00702-4",
language = "English",
volume = "31",
pages = "11819--11848",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "12",
}