Journal article
Conformal transformations and curvature
Journal of knot theory and its ramifications, Vol.28(2), p.1950020
02/01/2019
DOI: 10.1142/S0218216519500202
Abstract
In this paper, we discuss the relationship between conformal transformations of R-n U {infinity} and the curvature of curves. First, for any non-circular closed curve, there exists a length-preserving inversion such that the maximum pointwise absolute curvature can be made arbitrarily large. In contrast, we show that the total absolute curvatures of a family of curves conformally equivalent to a given simple or simple closed curve are uniformly bounded. Furthermore, we show that the total absolute curvature of an inverted regular C-2 simple closed curve as a function of inversion center and radius is removably discontinuous along the curve with exactly a 2 pi drop, and continuous elsewhere.
Details
- Title: Subtitle
- Conformal transformations and curvature
- Creators
- Richard G Ligo - Gannon UniversityOguz C Durumeric - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of knot theory and its ramifications, Vol.28(2), p.1950020
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- DOI
- 10.1142/S0218216519500202
- ISSN
- 0218-2165
- eISSN
- 1793-6527
- Number of pages
- 39
- Grant note
- University of Iowa Graduate College
- Language
- English
- Date published
- 02/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984241058602771
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