Displaying similar documents to “Existence results for the prescribed Scalar curvature on S 3 ”

The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions

Ursula Ludwig (2010)

Annales de l’institut Fourier

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In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular curve X and a stratified Morse function f . In this note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of f .

Puiseux series polynomial dynamics and iteration of complex cubic polynomials

Jan Kiwi (2006)

Annales de l’institut Fourier

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We let 𝕃 be the completion of the field of formal Puiseux series and study polynomials with coefficients in 𝕃 as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in 𝕃 [ ζ ] . We show that cubic polynomial dynamics over 𝕃 and ℂ are intimately related. More precisely, we establish that some elements of 𝕃 naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity)...

Critical points of asymptotically quadratic functions

Michal Fečkan (1995)

Annales Polonici Mathematici

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Existence results for critical points of asymptotically quadratic functions defined on Hilbert spaces are studied by using Morse-Conley index and pseudomonotone mappings. Applications to differential equations are given.

Equivariant maps of joins of finite G-sets and an application to critical point theory

Danuta Rozpłoch-Nowakowska (1992)

Annales Polonici Mathematici

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A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function f : S n → ℝ , where G is a finite nontrivial group acting freely and orthogonally on ℝ n + 1 0 . Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk’s Antipodal Theorem for equivariant maps of joins of G-sets.