Aperture of plane curves

Daisuke Kagatsume and Takashi Nishimura

Journal of Singularities
volume 12 (2015), 80-91

Received 21 April 2014. Received in revised form 21 August 2014.

DOI: 10.5427/jsing.2015.12e

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For any given C^\infty immersion r: S^1->R^2 such that the no-silhouette of r is not empty, a simple geometric model of crystal growth is constructed. It is shown that our geometric model of crystal growth never formulates a polygon while it is growing. Moreover, it is shown also that our model always dissolves to a point.


aperture, aperture angle, aperture point, Wulff shape

Mathematical Subject Classification:

58K30, 68T45, 82D25

Author(s) information:

Daisuke Kagatsume Takashi Nishimura
Machida Hall Research Group of Mathematical Sciences
Machida City Research Institute of Environment and
Tokyo 194-8520, Japan Information Sciences
Yokohama National University
Yokohama 240-8501, Japan
email: kagatsume-daisuke-mt@ynu.jp email: nishimura-takashi-yx@ynu.jp