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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 4, Pages 80–83
DOI: https://doi.org/10.4213/faa224 (Mi faa224) 		 
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On Functions Whose All Critical Points Are Contained in a Ball

P. E. Pushkar'

Independent University of Moscow
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DOI: https://doi.org/10.4213/faa224
Abstract: In the present note, we answer the following question posed by Arnold. Consider a function with finitely many critical points on a compact connected manifold without boundary. Suppose that a ball embedded in the manifold contains all critical points of the function. Is it possible to reconstruct the manifold by a restriction of the function to the ball? It turns out that one can reconstruct only the Euler characteristic of the manifold.
Keywords: Morse function, gradient-like vector field.
Received: 30.04.2002
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 4, Pages 321–323
DOI: https://doi.org/10.1023/A:1021774113006
Bibliographic databases:
Document Type: Article
UDC: 515.164.174
Language: Russian
Citation: P. E. Pushkar', “On Functions Whose All Critical Points Are Contained in a Ball”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 80–83; Funct. Anal. Appl., 36:4 (2002), 321–323
Citation in format AMSBIB
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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