Abstract
Motivated by a profound observation of A’Campo we investigate the behaviour of the curvature of $f(z,w)=c, f\in \mathbf{C}\{z,w\}, |c|$ small, along infinitesimals. We use the language of infinitesimals as introduced in [2]. Along the way we introduce the important notion of gradient canyon, and prove several theorems in which this notion plays the key role. In this paper we give three such theorems and mention several other facts, to be published elsewhere.
Citation
Satoshi Koike. Tzee-Char Kuo. Laurentiu Paunescu. "A study of curvature using infinitesimals." Proc. Japan Acad. Ser. A Math. Sci. 88 (5) 70 - 74, May 2012. https://doi.org/10.3792/pjaa.88.70
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