Hypersurfaces in \Bbb {R}^n and critical points in their external region

Author: Manchón P.M.G.

Source: Czechoslovak Mathematical Journal, Volume 52, Number 1, March 2002 , pp. 1-9(9)

Publisher: Springer

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Abstract:

In this paper we study the hypersurfaces M^n given as connected compact regular fibers of a differentiable map f : \Bbb {R}^{n+1} \rightarrow \Bbb R, in the cases in which f has finitely many nondegenerate critical points in the unbounded component of \Bbb {R}^{n+1} - M^n.

Keywords: hypersurface in \Bbb {R}^n; nondegenerate critical point; noncompact Morse Theory; h-cobordism; Palais-Smale condition

Language: English

Document Type: Research article

Affiliations: 1: Universidad Complutense, Facultad de Matemáticas, Dpto. de Geometría y Topología, Ciudad Universitaria s/n, 28040 Madrid, Spain, pmanchon@terra.es; pmanchon@ma.upm.es

Publication date: 2002-03-01