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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1611.09965 |
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| _version_ | 1866909334750887936 |
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| author | Moreira, Carlos Gustavo Ibarra, Sergio Augusto Romaña Silva, Waliston Luiz |
| author_facet | Moreira, Carlos Gustavo Ibarra, Sergio Augusto Romaña Silva, Waliston Luiz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_09965 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A generalization of Marstrand's theorem and some geometric applications Moreira, Carlos Gustavo Ibarra, Sergio Augusto Romaña Silva, Waliston Luiz Metric Geometry 28A80 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. |
| title | A generalization of Marstrand's theorem and some geometric applications |
| topic | Metric Geometry 28A80 |
| url | https://arxiv.org/abs/1611.09965 |