Dimensions of projections of sets on Riemannian surfaces of constant curvature (Q2802113)

In this paper the authors obtain generic lower bounds for the Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature.NEWLINENEWLINETo this aim, they apply the theory of \textit{Y. Peres} and \textit{W. Schlag} [Duke Math. J. 102, No. 2, 193--251 (2000; Zbl 0961.42007)] which provides a general abstract framework of generic Hausdorff dimension distortion results in metric spaces: their main result -- Theorem 1.1 -- depends on the verification of the crucial conditions of regularity and transversality of projections allowing the application of the results of Peres and Schlag. This is based on considerations using hyperbolic trigonometry for the case of negative curvature and spherical trigonometry for the case of positive curvature.NEWLINENEWLINEAs a conclusion they obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.