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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| Main Authors: | , , , |
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| 格式: | Article |
| 語言: | English |
| 出版: |
2022
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| 在線閱讀: | https://hdl.handle.net/10356/162510 |
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| 總結: | 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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