arXiv subjects

Waliston Luiz Silva

Publications and source records attributed to Waliston Luiz Silva.

2 recordsLinked to original sources

arXiv2024

A generalization of Marstrand's theorem and some geometric applications

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.

math.MG↗

arXiv2021

A generalization of Marstrand's theorem

In this paper we prove two general results related to Marstrand's projection theorem in a quite general formulation over separable metric spaces under a suitable transversality hypothesis (the "projections" are in principle only measurable) - the result is flexible enough to, in particular, recover most of the classical Marstrand-like theorems. Our proofs use simpler tools than many classical works in the subject, where some techniques from harmonic analysis or special geometrical structures on the spaces are used.

math.MG↗