Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Pablo Shmerkin"'
Autor:
Pablo Shmerkin, Han Yu
Publikováno v:
Discrete Analysis (2021)
On sets containing a unit distance in every direction, Discrete Analysis 2021:5, 13 pp. A _Kakeya set_ in $\mathbb R^d$ is a subset $A\subset\mathbb R^d$ that contains a line in every direction. Besicovitch famously proved that a Kakeya set in $\math
Externí odkaz:
https://doaj.org/article/f3186d00cf0543bebff7ca29faa390b8
Autor:
Pablo Shmerkin
Publikováno v:
Discrete Analysis (2017)
On distance sets, box-counting and Ahlfors-regular sets, Discrete Analysis 2017:9, 22 pp. A well-known problem of Falconer, a sort of continuous analogue of the Erdős distinct-distance problem, asks how large the Hausdorff dimension of a Borel subs
Externí odkaz:
https://doaj.org/article/f51bbf19e16c44dc806ac933f4ede3f3
Autor:
Pablo Shmerkin
Publikováno v:
Journal of the European Mathematical Society.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dc73d30636eb9e6a469f700beefeb19f
https://doi.org/10.4171/jems/1283
https://doi.org/10.4171/jems/1283
Publikováno v:
Revista Matemática Iberoamericana. 38:295-322
We show that given $\alpha \in (0, 1)$ there is a constant $c=c(\alpha) > 0$ such that any planar $(\alpha, 2\alpha)$-Furstenberg set has Hausdorff dimension at least $2\alpha + c$. This improves several previous bounds, in particular extending a res
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2e9fc11cb84754aa3d7bb6967e20f1d
https://doi.org/10.4171/rmi/1281
https://doi.org/10.4171/rmi/1281
Autor:
Pablo Shmerkin
Publikováno v:
Journal of Fractal Geometry. 8:27-51
We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than $1$, improving recent estimates of Keleti and Shmerkin, and of Liu in this regime. In particular, w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43cf57433e6d7b43e46ffbc5d1a2f6a8
https://doi.org/10.4171/jfg/97
https://doi.org/10.4171/jfg/97
Autor:
Pablo Shmerkin, Ville Suomala
We prove $L^p$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. {\L}aba and M. Pramanik and in some cases are sharp up to the endpoint. A consequence of our
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f070e18aff7f6cc6ddd5249f458833c
http://arxiv.org/abs/2106.14818
http://arxiv.org/abs/2106.14818
Autor:
Eino Rossi, Pablo Shmerkin
Publikováno v:
CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
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 th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea5b188d31c72d5edbd9a0d9ef27c18f
https://doi.org/10.4171/jfg/78
https://doi.org/10.4171/jfg/78
Publikováno v:
Oberwolfach Reports. 14:2847-2905
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fe9a54f10e80437c64f77429b21b6e60
https://doi.org/10.4171/owr/2017/47
https://doi.org/10.4171/owr/2017/47
Autor:
Eino Rossi, Pablo Shmerkin
The $L^q$ dimensions, for $1
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::91ed89aba7ef1c632c561044cabd158c
http://hdl.handle.net/10138/325288
http://hdl.handle.net/10138/325288
Autor:
Pablo Shmerkin, Ian Morris
Publikováno v:
Transactions of the American Mathematical Society. 371:1547-1582
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-affine proper subsets of the original set. These self-affine subsets m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3edeaba58ef1d89d21c48a9b9dddbbb0
https://doi.org/10.1090/tran/7334
https://doi.org/10.1090/tran/7334