Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/162510
Title: Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics
Authors: Bauer, Martin
Bruveris, Martins
Harms, Philipp
Michor, Peter W.
Keywords: Science::Mathematics
Issue Date: 2022
Source: Bauer, M., Bruveris, M., Harms, P. & Michor, P. W. (2022). Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics. Communications in Mathematical Physics, 389(2), 899-931. https://dx.doi.org/10.1007/s00220-021-04264-y
Journal: Communications in Mathematical Physics
Abstract: We show for a certain class of operators A and holomorphic functions f that the functional calculus A↦ f(A) is holomorphic. Using this result we are able to prove that fractional Laplacians (1+Δg)p depend real analytically on the metric g in suitable Sobolev topologies. As an application we obtain local well-posedness of the geodesic equation for fractional Sobolev metrics on the space of all Riemannian metrics.
URI: https://hdl.handle.net/10356/162510
ISSN: 0010-3616
DOI: 10.1007/s00220-021-04264-y
Rights: © The Author(s) 2021 under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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