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arXiv · 1810.03169

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

Martin Bauer·Martins Bruveris·Philipp Harms·Peter W. Michor
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Abstract

We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ 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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Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor. 2018-10-07. Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics. https://doi.org/10.1007/s00220-021-04264-y

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