Preservation of Immersed or Injective Properties by Composing Generic Generalized Distance-Squared Mappings

  • Shunsuke Ichiki
  • Takashi NishimuraEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)


Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalized distance-squared mapping of equidimensional case is not injective. Nevertheless, in this paper, it is shown that the immersed property or the injective property of a mapping is preserved by composing a generic generalized distance-squared mapping of equidimensional case.


Generalized distance-squared mapping Immersion Injective Embedding Transverse 

2010 Mathematics Subject Classification

57R35 57R40 57R42 



The authors are most grateful to the anonymous reviewer for his/her careful reading of the first manuscript of this paper and invaluable suggestions. The first author is supported by JSPS KAKENHI Grant Number 16J06911.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Environment and Information SciencesYokohama National UniversityYokohamaJapan
  2. 2.Research Group of Mathematical Sciences, Research Institute of Environment and Information SciencesYokohama National UniversityYokohamaJapan

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