Methods and Applications of Analysis
Volume 25 (2018)
In Memory of Professor John N. Mather: Part 2 of 3
Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.
Transversality theorems on generic linearly perturbed mappings
Pages: 323 – 336
In his celebrated paper “Generic projections”, John Mather has given a striking transversality theorem and its applications on generic projections. On the other hand, in this paper, two transversality theorems on generic linearly perturbed $C^r$ mappings are shown $(r \geq 1)$. Moreover, some applications of the two theorems are also given.
generic linear perturbation, transversality, immersion, injection
2010 Mathematics Subject Classification
The author was supported by JSPS KAKENHI Grant Numbers JP16J06911 and JP19J00650.
Received 13 June 2018
Accepted 6 August 2018
Published 1 November 2019