Visible parts and dimensions

Nonlinearity

Volumn 16, Issue 3, 2003, Pages 803-818

  Järvenpää, Esa ^a   Järvenpää, Maarit ^a   MacManus, Paul ^b   O'Neil, Toby C ^c  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

^b Phillips Exeter Academy   (United States)

^c OPEN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242340419     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/3/302     Document Type: Article

References (15)

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3. [Ce] Cel J 1997 An optimal Krasnoselskii-type theorem for an open starshaped set Geom. Dedicata 66 293-301
4. [Cs] Csörnyei M 2000 On the visibility of invisible sets An. Acad. Sci. Fenn. Math. 25 417-21
5. [Cu] Cutler C D 1995 Strong and weak duality principles for fractal dimension in Euclidean space Math. Proc. Camb. Phil. Soc. 118 393-410
6. Davies R and Fast H 1978 Lebesgue density influences Hausdorff measure; large sets surface-like from many directions Mathematika 25 116-9
7. Davis F 1997 Is the universe homogeneous on large scales? Critical Dialogues in Cosmology ed N Turok (Singapore: World Scientific)
8. [F] Falconer K J 1977 The dimension of the convex kernel of a compact starshaped set Bull. Lond. Math. Soc. 9 313-6
9. [JJN] Järvenpää E, Järvenpää M and Niemelä J Transversal mappings between manifolds and non-trivial measures on visible parts In preparation
10. [JM] Järvenpää M and Mattila P 1998 Hausdorff and packing dimensions and sections of measures Mathematika 45 55-77
11. [Mat] Marstrand J 1954 Some fundamental geometric properties of plane sets of fractional dimension P roc. Lond. Math. Soc. 4 257-301
12. [Mat] Mattila P 1995 Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability (Cambridge: Cambridge University Press)
13. [Mc] McMullen C 1984 The Hausdorff dimension of general Sierpiński carpets Nagoya Math. J. 96 1-9
14. [PS] Peres Y and Schlag W 2000 Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions Duke Math. J. 102 193-251
15. [PMS] Pietronero L, Montuori M and Sylos Labini F 1997 On the fractal structure of the visible universe Critical Dialogues in Cosmology ed N Turok (Singapore: World Scientific)