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On functions whose all critical points are contained in a ball

par Pushkar, Petr
Référence Functional analysis and its applications, 36, 4, page (321-323)
Publication Publié, 2002

Article révisé par les pairs

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Résumé :

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.