Spectral rigidity and invariant distributions on Anosov surfaces
Paternain, G. P., Salo, M., & Uhlmann, G. (2014). Spectral rigidity and invariant distributions on Anosov surfaces. Journal of differential geometry, 98(1), 147-181. https://doi.org/10.4310/jdg/1406137697
Published in
Journal of differential geometryDate
2014Copyright
© The Authors. © Lehigh University, 2014. This is an authors' final draft version of an article whose final and definitive form has been published by Lehigh University. Published in this repository with the kind permission of the publisher.
This article considers inverse problems on closed Riemannian surfaces whose geodesic
flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the
geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results
for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity
results are of independent interest and imply the existence of many geometric invariant
distributions on the unit sphere bundle. In particular, we show that on any Anosov
surface (M,g), given a smooth function f on M there is a distribution in the Sobolev
space H-1(SM) that is invariant under the geodesic flow and whose projection to M
is the given function f.
Publisher
Lehigh UniversityISSN Search the Publication Forum
0022-040XKeywords
Original source
http://projecteuclid.org/euclid.jdg/1406137697Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/23817354
Metadata
Show full item recordCollections
Related items
Showing items with similar title or keywords.
-
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther (Springer Berlin Heidelberg, 2015)In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ... -
Remote Sensing of 3-D Geometry and Surface Moisture of a Peat Production Area Using Hyperspectral Frame Cameras in Visible to Short-Wave Infrared Spectral Ranges Onboard a Small Unmanned Airborne Vehicle (UAV)
Honkavaara, Eija; Eskelinen, Matti; Pölönen, Ilkka; Saari, Heikki; Ojanen, Harri; Mannila, Rami; Holmlund, Christer; Hakala, Teemu; Litkey, Paula; Rosnell, Tomi; Viljanen, Niko; Pulkkanen, Merja (Institute of Electrical and Electronics Engineers, 2016)Miniaturized hyperspectral imaging sensors are becoming available to small unmanned airborne vehicle (UAV) platforms. Imaging concepts based on frame format offer an attractive alternative to conventional hyperspectral ... -
Assessment of microalgae species, biomass and distribution from spectral images using a convolution neural network
Salmi, Pauliina; Pölönen, Ilkka; Pääkkönen, Salli; Taipale, Sami; Calderini, Marco (University of Jyväskylä, 2021-11-08)Artikkeliin "Assessment of microalgae species, biomass and distribution from spectral images using a convolution neural network" liittyvä aineisto koostuu seuraavista osista: 1.Transmittanssi-hyperspektrikuvat levänäytteistä ... -
Assessment of microalgae species, biomass, and distribution from spectral images using a convolution neural network
Salmi, Pauliina; Calderini, Marco; Pääkkönen, Salli; Taipale, Sami; Pölönen, Ilkka (Springer Science and Business Media LLC, 2022)Effective monitoring of microalgae growth is crucial for environmental observation, while the applications of this monitoring could also be expanded to commercial and research-focused microalgae cultivation. Currently, the ... -
Analyzing Measurement Invariance of the Students’ Engagement Instrument Brief Version : The Cases of Denmark, Finland, and Portugal
Virtanen, Tuomo; Moreira, P.; Ulvseth, H.; Andersson, H.; Tetler, S.; Kuorelahti, Matti (Sage Publications, Inc., 2018)The promotion of students’ engagement with school is an internationally acknowledged challenge in education. There is a need to examine the structure of the concept of student engagement and to discover the best practices ...