A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of a given plane curve and generic distance-squared mappings on the plane into the plane are investigated from the viewpoint of stability.
The author was supported by JSPS KAKENHI Grant Numbers JP16J06911
The author is most grateful to the anonymous reviewer for carefully reading the first manuscript of this paper and for giving invaluable suggestions. The author is grateful to Takashi Nishimura for his kind comments.
"Generic distance-squared mappings on plane curves." Hiroshima Math. J. 51 (1) 65 - 76, March 2021. https://doi.org/10.32917/h2020010