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## Banach Center Publications

1999 | 50 | 1 | 91-105
Tytuł artykułu

### The centre symmetry set

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A centrally symmetric plane curve has a point called it's centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^3$. We investigate some of it's properties, and begin the study of non-convex cases.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
91-105
Opis fizyczny
Daty
wydano
1999
Twórcy
autor
• Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
autor
• Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
Bibliografia
• [1] V. I. Arnol'd, Critical points of functions on a manifold with boundary, the simple Lie groups $B_k$, $C_k$, and $F_4$ and singularities of evolutes (in Russian), Uspekhi Mat. Nauk 33 no. 5 (1978), 91-105, 237; English transl.: Russian Math. Surveys 33 no. 5 (1978), 99-116.
• [3] J. W. Bruce and P. J. Giblin, Growth, motion and 1-parameter families of symmetry sets, Proc. Roy. Soc. Edinburgh Sect. A 104 (1986), 179-204.
• [4] J. W. Bruce and P. J. Giblin, Projections of surfaces with boundary, Proc. London Math. Soc. (3) 60 (1990), 392-416.
• [2] J. W. Bruce, P. J. Giblin and C. G. Gibson, Symmetry sets, Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), 163-186.
• [6] P. J. Giblin and S. A. Brassett, Local symmetry of plane curves, Amer. Math. Monthly 92 (1985), 689-707.
• [7] P. J. Giblin and G. Sapiro, Affine-invariant distances, envelopes and symmetry sets, Geom. Dedicata 71 (1998), 237-261.
• [8] V. V. Goryunov, Projections of generic surfaces with boundary, in: Theory of Singularities and its Applications, V. I. Arnol'd (ed.), Adv. Soviet Math. 1, Amer. Math. Soc., Providence, 1990, 157-200.
• [9] P. Holtom, Local Central Symmetry for Euclidean Plane Curves, M.Sc. Dissertation, University of Liverpool, Sept. 1997.
• [10] S. Janeczko, Bifurcations of the center of symmetry, Geom. Dedicata 60 (1996), 9-16.
• [11] Liverpool Surface Modelling Package, written by Richard Morris for Silicon Graphics and X Windows. See R. J. Morris, The use of computer graphics for solving problems in singularity theory, in: Visualization in Mathematics, H.-C. Hege and K. Polthier (eds.), Springer, Heidelberg, 1997, 53-66.
• [5] Buchin Su, Affine Differential Geometry, Science Press, Beijing; Gordon and Breach, New York, 1983.
• [12] V. M. Zakalyukin, Envelopes of families of wave fronts and control theory, Proc. Steklov Inst. Math. 209 (1995), 114-123.
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Bibliografia
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