Projection and slicing theorems in Heisenberg groups

Balogh, Zoltán M.; Fässler, Katrin; Mattila, Pertti; Tyson, Jeremy T.

doi:10.1016/j.aim.2012.03.037

Cited by 33 publications

(66 citation statements)

References 9 publications

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“…The projection theorem for G h (d, m) is due to Z. Balogh, K. Fässler, P. Mattila and J. Tyson [1]; a different proof based on the notion of transversality was given by R. Hovila [5].…”

Section: Introductionmentioning

confidence: 98%

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Hausdorff dimension estimates for restricted families of projections in R3

Orponen

2015

Advances in Mathematics

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This paper is concerned with restricted families of projections in R 3 . Let K ⊂ R 3 be a Borel set with Hausdorff dimension dim K = s > 1. If G is a smooth and sufficiently wellcurved one-dimensional family of two-dimensional subspaces, the main result states that there exists σ(s) > 1 such that dim π V (K) ≥ σ(s) for almost all V ∈ G. A similar result is obtained for some specific families of one-dimensional subspaces.

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“…The projection theorem for G h (d, m) is due to Z. Balogh, K. Fässler, P. Mattila and J. Tyson [1]; a different proof based on the notion of transversality was given by R. Hovila [5].…”

Section: Introductionmentioning

confidence: 98%

“…Write θ := span(γ(θ)) ∈ G (3,1), and V θ := ⊥ θ ∈ G (3,2). Then, the families { θ } θ∈J and {V θ } θ∈J are referred to as non-degenerate families of lines and planes, respectively.…”

Section: Introductionmentioning

confidence: 99%

Hausdorff dimension estimates for restricted families of projections in R3

Orponen

2015

Advances in Mathematics

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“…There are various other results in the papers [BD13,BF12]. In local coordinates for V the expression a − 2ω(v, P V (w)) is a second degree polynomial which can vanish to second order.…”

Section: This Is Sharp: Considermentioning

confidence: 97%

“…Let us now consider higher dimensions, these were treated in [BF12]. Then the basic notions and facts are…”

Section: This Is Sharp: Considermentioning

confidence: 99%

Geometry and Analysis of Fractals

Ding¹,

Lau²

2014

Springer Proceedings in Mathematics &Amp; Statistics

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This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.More information about this series at

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“…It remains to show that H t ∞ (R) r 6−t 1 r 2(t−3) 2 for r 1 ≥ r 2 and t ∈ [3,4]. This is done by estimating the Hausdorff content of annuli of the form…”

Section: Hausdorff Content and Energy Of Rectangles In Hmentioning

confidence: 99%