Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Andreas Bernig; Dmitry Faifman; Gil Solanes

doi:10.1007/s12220-021-00702-4

Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Andreas Bernig^*, Dmitry Faifman, Gil Solanes

^*Corresponding author for this work

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

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 Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

Original language	English
Pages (from-to)	11819-11848
Number of pages	30
Journal	Journal of Geometric Analysis
Volume	31
Issue number	12
DOIs	https://doi.org/10.1007/s12220-021-00702-4
Publication status	Published - Dec 2021

Keywords

Curvature measure
Lipschitz–Killing measures
Pseudo-Riemannian manifolds
Valuation
Weyl principle

Access to Document

10.1007/s12220-021-00702-4

Cite this

@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",

}

TY - JOUR

T1 - Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

AU - Bernig, Andreas

AU - Faifman, Dmitry

AU - Solanes, Gil

N1 - 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 Húnter Programme. Publisher Copyright: © 2021, The Author(s).

PY - 2021/12

Y1 - 2021/12

N2 - 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 Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

AB - 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 Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

KW - Curvature measure

KW - Lipschitz–Killing measures

KW - Pseudo-Riemannian manifolds

KW - Valuation

KW - Weyl principle

UR - http://www.scopus.com/inward/record.url?scp=85107891337&partnerID=8YFLogxK

U2 - 10.1007/s12220-021-00702-4

DO - 10.1007/s12220-021-00702-4

M3 - Article

AN - SCOPUS:85107891337

SN - 1050-6926

VL - 31

SP - 11819

EP - 11848

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 12

ER -

Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this