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dc.contributor.author
Shmerkin, Pablo Sebastian
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dc.date.available
2022-09-26T19:36:23Z
dc.date.issued
2020-12
dc.identifier.citation
Shmerkin, Pablo Sebastian; Improved bounds for the dimensions of planar distance sets; European Mathematical Society; Journal of Fractal Geometry; 8; 1; 12-2020; 27-51
dc.identifier.uri
http://hdl.handle.net/11336/170509
dc.description.abstract
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, we prove that if dimH .A/ > 1, then the set of distances spanned by points of A has Hausdorff dimension at least 40=57 > 0:7 and there are many y 2 A such that the pinned distance set 1jx -yjW x 2 Aºhas Hausdorff dimension at least 29=42 and lower box-counting dimension at least 40=57. We use the approach and many results from the earlier work of Keleti and Shmerkin, but incorporate estimates from the recent work of Guth, Iosevich, Ou and Wang as additional input.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
European Mathematical Society
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/
dc.subject
BOX COUNTING DIMENSION
dc.subject
DISTANCE SETS
dc.subject
FALCONER’S PROBLEM
dc.subject
HAUSDORFF DIMENSION
dc.subject
PINNED DISTANCE SETS
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Improved bounds for the dimensions of planar distance sets
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-09-23T15:42:13Z
dc.identifier.eissn
2308-1309
dc.journal.volume
8
dc.journal.number
1
dc.journal.pagination
27-51
dc.journal.pais
Alemania
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dc.journal.ciudad
Berlín
dc.description.fil
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. University of British Columbia; Canadá
dc.journal.title
Journal of Fractal Geometry
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/doi/10.4171/JFG/97
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4171/JFG/97
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