Daniel Cibotaru
Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods
Cibotaru, Daniel; Galaz-García, Fernando
Abstract
Kurdyka–Łojasiewicz (KŁ) functions are real-valued functions characterized by a differential inequality involving the norm of their gradient. This class of functions is quite rich, containing objects as diverse as subanalytic, transnormal or Morse functions. We prove that the zero locus of a Kurdyka–Łojasiewicz function admits a mapping cylinder neighborhood. This implies, in particular, that wildly embedded topological 2-manifolds in 3-dimensional Euclidean space, such as Alexander horned spheres, do not arise as the zero loci of KŁ functions.
Citation
Cibotaru, D., & Galaz-García, F. (in press). Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods. Annales de l'Institut Fourier,
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 23, 2022 |
Deposit Date | Sep 26, 2022 |
Publicly Available Date | Mar 29, 2024 |
Journal | Annales de l'Institut Fourier |
Print ISSN | 0373-0956 |
Electronic ISSN | 1777-5310 |
Publisher | Association des Annales de l'Institut Fourier |
Peer Reviewed | Peer Reviewed |
Public URL | https://durham-repository.worktribe.com/output/1191190 |
Publisher URL | https://aif.centre-mersenne.org/ |
You might also like
Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature
(2022)
Journal Article
Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric
(2020)
Journal Article
Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey
(2020)
Book Chapter
Cohomogeneity one Alexandrov spaces in low dimensions
(2020)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search