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Sergio Augusto Romaña Ibarra

Publications and source records attributed to Sergio Augusto Romaña Ibarra.

5 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

On the Lagrange and Markov Dynamical Spectra for Anosov Flows in dimension 3

We consider the Lagrange and the Markov dynamical spectra associated with a conservative Anosov flow on a compact manifold of dimension $3$ (including geodesic flows of negative curvature and suspension flows). We show that for a large set of real functions and typical conservative Anosov flows, both the Lagrange and Markov dynamical spectra have a non-empty interior.

math.DS↗
arXiv2015

On the Lagrange and Markov Dynamical Spectra

We consider the Lagrange and the Markov dynamical spectra associated to horseshoes on surface with Hausdorff dimensions greater than 1. We show that for a "large" set of real functions on the surface and for "typical" horseshoes with Hausdorff dimensions greater than 1, then both the Lagrange and the Markov dynamical spectrum have persistently non-empty interior.

math.DS↗
arXiv2014

The Marstrand Theorem in Nonpositive Curvature

In a paper from 1954, Marstrand proved that if $K\subset \mathbb{R}^2$ with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we show that if $M$ is a simply connected surface with non-positive curvature, then Marstrand's theorem is still valid.

math.DG↗