Dimensions of projections of sets on Riemannian surfaces of constant curvature

Balogh, Zoltán; Iseli, Annina

doi:10.1090/proc/12934

Dimensions of projections of sets on Riemannian surfaces of constant curvature
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by Zoltán M. Balogh and Annina Iseli PDF

Proc. Amer. Math. Soc. 144 (2016), 2939-2951 Request permission

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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