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March 2021 Equivalence of Kuo and Thom quantities for analyticfunctions
Karim Bekka, Satoshi Koike
Proc. Japan Acad. Ser. A Math. Sci. 97(3): 19-24 (March 2021). DOI: 10.3792/pjaa.97.004

Abstract

Sufficiency of jets is a very important notion introduced by René Thom in order to establish the structural stability theory. The criteria for some sufficiency of jets are known as the Kuo condition and Thom type inequality, which are defined using the Kuo quantity and Thom quantity. Therefore these quantities are meaningful. In this paper we show the equivalence of Kuo and Thom quantities. Then we apply this result to the relative conditions to a given closed set.

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Karim Bekka. Satoshi Koike. "Equivalence of Kuo and Thom quantities for analyticfunctions." Proc. Japan Acad. Ser. A Math. Sci. 97 (3) 19 - 24, March 2021. https://doi.org/10.3792/pjaa.97.004

Information

Published: March 2021
First available in Project Euclid: 17 March 2021

Digital Object Identifier: 10.3792/pjaa.97.004

Subjects:
Primary: 57R45
Secondary: 58K40

Keywords: Kuo condition , Kuo quantity , sufficiency of jet , Thom quantity , Thom type inequality

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 3 • March 2021
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