The Library
How large dimension guarantees a given angle?
Tools
Harangi, Viktor, Keleti, Tamás, Kiss, Gergely, Maga, Péter, Máthé, András, Mattila, Pertti and Strenner, Balázs (2013) How large dimension guarantees a given angle? Monatshefte fuer Mathematik, Volume 171 (Number 2). pp. 169-187. doi:10.1007/s00605-012-0455-0 ISSN 0026-9255.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1007/s00605-012-0455-0
Abstract
We study the following two problems: (1) Given n≥ 2 and 0≤ α ≤ 180°, how large Hausdorff dimension can a compact set A ⊂ ℝn have if A does not contain three points that form an angle α? (2) Given α and δ, how large Hausdorff dimension can a subset A of a Euclidean space have if A does not contain three points that form an angle in the δ-neighborhood of α? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and 180°, the angles 60°, 90° and 120° also play special role in problem (2): the maximal dimension is smaller for these angles than for the other angles. In problem (1) the angle 90° seems to behave differently from other angles.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Monatshefte fuer Mathematik | ||||
Publisher: | Springer Verlag | ||||
ISSN: | 0026-9255 | ||||
Official Date: | 1 August 2013 | ||||
Dates: |
|
||||
Volume: | Volume 171 | ||||
Number: | Number 2 | ||||
Page Range: | pp. 169-187 | ||||
DOI: | 10.1007/s00605-012-0455-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |