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Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods

Cibotaru, Daniel and Galaz-García, Fernando 'Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods.', Annales de l'Institut Fourier .


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
Publisher Web site:
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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