Dimensions of projections of sets on Riemannian surfaces of constant curvature
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- by Zoltán M. Balogh and Annina Iseli PDF
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Abstract:
We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand’s theorem, Kaufman’s theorem, and Falconer’s theorem in the above geometrical settings.References
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Additional Information
- Zoltán M. Balogh
- Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- Email: zoltan.balogh@math.unibe.ch
- Annina Iseli
- Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- Email: annina.iseli@math.unibe.ch
- Received by editor(s): July 15, 2015
- Received by editor(s) in revised form: August 14, 2015
- Published electronically: November 6, 2015
- Additional Notes: This research was partially supported by the Swiss National Science Foundation
- Communicated by: Jeremy Tyson
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2939-2951
- MSC (2010): Primary 28A78
- DOI: https://doi.org/10.1090/proc/12934
- MathSciNet review: 3487226