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arXiv · 1402.5133

The Marstrand Theorem in Nonpositive Curvature

Sergio Augusto Romaña Ibarra
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Abstract

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.

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Sergio Augusto Romaña Ibarra. 2014-01-23. The Marstrand Theorem in Nonpositive Curvature. https://arxiv.org/abs/1402.5133

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