Dimensions of projections of sets on Riemannian surfaces of constant curvature

Balogh, Zoltan; Iseli, Annina (2016). Dimensions of projections of sets on Riemannian surfaces of constant curvature. Proceedings of the American Mathematical Society, 144(7), pp. 2939-2951. American Mathematical Society 10.1090/proc/12934

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Text AMS_PROC_150715 .pdf - Accepted Version Available under License Publisher holds Copyright. First published in Proc. Amer. Math. Soc. 144 (2016), 2939-2951, published by the American Mathematical Society Download (295kB) | Preview

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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