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

• 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
• Institution: Nanyang Technological University

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...