Open Access
May 2012 A study of curvature using infinitesimals
Satoshi Koike, Tzee-Char Kuo, Laurentiu Paunescu
Proc. Japan Acad. Ser. A Math. Sci. 88(5): 70-74 (May 2012). DOI: 10.3792/pjaa.88.70


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.


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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.


Published: May 2012
First available in Project Euclid: 7 May 2012

zbMATH: 1250.30043
MathSciNet: MR2925285
Digital Object Identifier: 10.3792/pjaa.88.70

Primary: 14Hxx , 32Sxx , 58K60
Secondary: 58K40

Keywords: curvature , gradient canyon , Lojasiewicz exponent , Newton-Piuseux field , Newton-Puiseux infinitesimals

Rights: Copyright © 2012 The Japan Academy

Vol.88 • No. 5 • May 2012
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