Reference : Scattering theory without injectivity radius assumptions and spectral stability for t...
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/32162
Scattering theory without injectivity radius assumptions and spectral stability for the Ricci flow
English
Güneysu, Batu [Humboldt-Universität zu Berlin > Institut für Mathematik]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
5-Sep-2017
15
No
[en] We prove a completely new integral criterion for the existence and completeness of the wave operators W_{\pm}(-\Delta_h,-\Delta_g, I_{g,h}) corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami operators -\Delta_j, j=g,h, that are induced by two quasi-isometric complete Riemannian metrics g and h on an open manifold M. In particular, this result provides a criterion for the absolutely continuous spectra of -\Delta_g and -\Delta_h to coincide. Our proof relies on estimates that are obtained using a probabilistic Bismut type formula for the gradient of a heat semigroup. Unlike all previous results, our integral criterion only requires some lower control on the Ricci curvatures and some upper control on the heat kernels, but no control at all on the injectivity radii. As a consequence, we obtain a stability result for the absolutely continuous spectrum under a Ricci flow.
Researchers
http://hdl.handle.net/10993/32162
https://arxiv.org/abs/1709.01612
http://arxiv.org/abs/1709.01612
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry Of Random Evolutions > 01/03/2015 > 28/02/2018 > 2014

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