Hölder coverings of sets of small dimension

@article{Rossi2017HlderCO,
  title={H{\"o}lder coverings of sets of small dimension},
  author={Eino Rossi and Pablo Shmerkin},
  journal={Journal of Fractal Geometry},
  year={2017}
}
We show that a set of small box counting dimension can be covered by a H\"older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe that, as a consequence, H\"older graphs can have positive doubling measure, answering a question of T. Ojala and T. Rajala. We also give remarks on H\"older coverings in polar coordinates and, on the other hand, prove that a Homogenous set of small… 
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4 Citations

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