Cibotaru, Daniel and Galaz-García, Fernando 'Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods.', Annales de l'Institut Fourier .
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.
| Item Type: | Article |
|---|---|
| Full text: | Publisher-imposed embargo (AM) Accepted Manuscript File format - PDF (493Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://aif.centre-mersenne.org/ |
| Date accepted: | 23 September 2022 |
| Date deposited: | 27 September 2022 |
| Date of first online publication: | No date available |
| Date first made open access: | No date available |
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