Displaying similar documents to “Some existence results for the scalar curvature problem via Morse theory”

Topological tools for the prescribed scalar curvature problem on S n

Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane (2014)

Open Mathematics

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In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Silvia Cingolani, Giuseppina Vannella (2001)

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

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We present critical groups estimates for a functional f defined on the Banach space W 0 1 , p ⁢ Ω , Ω bounded domain in R N , 2 < p < ∞ , associated to a quasilinear elliptic equation involving p -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of f in each critical point, we compute the critical groups of f in each isolated critical point via Morse index.

Multiplicity results for the prescribed scalar curvature on low spheres

Mohamed Ben Ayed, Mohameden Ould Ahmedou (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres 𝕊 3 , 𝕊 4 . Under generic conditions we establish some, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its to the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence result on 𝕊 4 through an Euler-Hopf type formula. ...

Curvature measures and fractals

Steffen Winter

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Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the ’classical’ concepts of curvature are not directly applicable to fractal sets. We try to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets F ⊆ ℝ d (e.g. fractals), for which classical geometric characteristics such as curvatures or Euler characteristic...

On the motion of a curve by its binormal curvature

Jerrard, Robert L., Didier Smets (2015)

Journal of the European Mathematical Society

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We propose a weak formulation for the binormal curvature flow of curves in ℝ 3 . This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to hold, as long as self-intersections do not occur. We also prove a global existence theorem in that framework.