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Type: Journal article
Title: Asymptotic expansions and conformal covariance of the mass of conformal differential operators
Author: Ludewig, M.
Citation: Annals of Global Analysis and Geometry, 2017; 52(3):237-268
Publisher: Springer
Issue Date: 2017
ISSN: 0232-704X
Statement of
Matthias Ludewig
Abstract: We give an explicit description of the full asymptotic expansion of the Schwartz kernel of the complex powers of m-Laplace type operators L on compact Riemannian manifolds in terms of Riesz distributions. The constant term in this asymptotic expansion turns out to be given by the local zeta function of L. In particular, the constant term in the asymptotic expansion of the Green’s function L−1 is often called the mass of L, which (in case that L is the Yamabe operator) is an important invariant, namely a positive multiple of the ADM mass of a certain asymptotically flat manifold constructed out of the given data. We show that for general conformally invariant m-Laplace operators L (including the GJMS operators), this mass is a conformal invariant in the case that the dimension of M is odd and that kerL=0, and we give a precise description of the failure of the conformal invariance in the case that these conditions are not satisfied.
Keywords: Laplace type operator; elliptic operator; Green’s function; Zeta function; heat kernel; conformal geometry; positive mass
Rights: © The Author(s) 2017. This article is an open access publication. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
RMID: 0030101043
DOI: 10.1007/s10455-017-9556-2
Appears in Collections:Mathematical Sciences publications

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