Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics

Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics

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 l...

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Bibliographic Details
Main Authors: Bauer, Martin, Bruveris, Martins, Harms, Philipp, Michor, Peter W.
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Science::Mathematics
Riemannian Geometry
Holomorphic Functions
Online Access:https://hdl.handle.net/10356/162510
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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