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Dimensions of projections of sets on Riemannian surfaces of constant curvature


Authors: Zoltán M. Balogh and Annina Iseli
Journal: Proc. Amer. Math. Soc. 144 (2016), 2939-2951
MSC (2010): Primary 28A78
DOI: https://doi.org/10.1090/proc/12934
Published electronically: November 6, 2015
MathSciNet review: 3487226
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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.


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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

DOI: https://doi.org/10.1090/proc/12934
Keywords: Hausdorff dimension, orthogonal projections
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
Article copyright: © Copyright 2015 American Mathematical Society