A generalization of Marstrand's theorem and some geometric applications

2016/11/30 by Moreira, Carlos Gustavo, Ibarra, Sergio Augusto Romaña, Silva, Waliston Luiz
#28A80 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1611.09965

Abstract

In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand's projection theorem in a quite general formulation over metric spaces under a suitable transversality condition (the "projections" are in principle only continuous, and the transversality condition gives flexibility in exponents) - the result is flexible enough to, in particular, recover most of the classical Marstrand-like theorems. We also give some new geometrical applications of our results - one of them is a new result related to Falconer's distance conjecture.

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