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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/162510 |
| _version_ | 1826112978012864512 |
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| author | Bauer, Martin Bruveris, Martins Harms, Philipp Michor, Peter W. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bauer, Martin Bruveris, Martins Harms, Philipp Michor, Peter W. |
| author_sort | Bauer, Martin |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T03:15:40Z |
| format | Journal Article |
| id | ntu-10356/162510 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:15:40Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1625102022-10-26T02:56:02Z Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics Bauer, Martin Bruveris, Martins Harms, Philipp Michor, Peter W. School of Physical and Mathematical Sciences Science::Mathematics Riemannian Geometry Holomorphic Functions 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. MB was partially supported by NSF-grants 1912037 and 1953244. PH was partially supported in the form of a Junior Fellowship of the Freiburg Institute of Advances Studies. 2022-10-26T02:56:01Z 2022-10-26T02:56:01Z 2022 Journal Article 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 0010-3616 https://hdl.handle.net/10356/162510 10.1007/s00220-021-04264-y 2-s2.0-85122655630 2 389 899 931 en Communications in Mathematical Physics © The Author(s) 2021 under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. |
| spellingShingle | Science::Mathematics Riemannian Geometry Holomorphic Functions Bauer, Martin Bruveris, Martins Harms, Philipp Michor, Peter W. Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics |
| title | Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics |
| title_full | Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics |
| title_fullStr | Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics |
| title_full_unstemmed | Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics |
| title_short | Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics |
| title_sort | smooth perturbations of the functional calculus and applications to riemannian geometry on spaces of metrics |
| topic | Science::Mathematics Riemannian Geometry Holomorphic Functions |
| url | https://hdl.handle.net/10356/162510 |
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