Displaying similar documents to “About the Euler-Poincaré characteristic of semi-algebraic sets defined with two inequalities.”

Equivalence of differentiable functions, rational functions and polynomials

Masahito Shiota (1982)

Annales de l'institut Fourier

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We show under some assumptions that a differentiable function can be transformed globally to a polynomial or a rational function by some diffeomorphism. One of the assumptions is that the function is proper, the number of critical points is finite, and the Milnor number of the germ at each critical point is finite.

Prescribing Q -curvature on higher dimensional spheres

Khalil El Mehdi (2005)

Annales mathématiques Blaise Pascal

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We study the problem of prescribing a fourth order conformal invariant on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results.

Some perturbation results for non-linear problems

Carlo Carminati (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.