Marstrand type projection theorems for normed spaces

Balogh, Zoltan; Iseli, Annina (2018). Marstrand type projection theorems for normed spaces (In Press). Journal of Fractal Geometry EMS Publishing House

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We consider Marstrand type projection theorems for closest-point projections in the normed space ℝ². We prove that if a norm on ℝ² is regular enough, then the analogues of the well-known statements from the Euclidean setting hold, while they fail for norms whose unit balls have corners. We establish our results by verifying Peres and Schlag’s transversality property and thereby also obtain a Besicovitch-Federer type characterization of purely unrectifiable sets

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan and Iseli, Annina

Subjects:

500 Science > 510 Mathematics

ISSN:

2308-1317

Publisher:

EMS Publishing House

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

10 May 2019 12:04

Last Modified:

10 May 2019 12:04

ArXiv ID:

1802.10563v1

BORIS DOI:

10.7892/boris.125488

URI:

https://boris.unibe.ch/id/eprint/125488

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