Browsing by Author "Ndiaye, Cheikh Birahim"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Constant T-curvature conformal metrics on 4-manifolds with boundary
    (2007-08-07T12:10:17Z) Ndiaye, Cheikh Birahim; Mathematics; Functional Analysis and Applications
    In this paper we prove that, given a compact four dimensional smooth Riemannian manifold (M,g) with smooth boundary there exists a metric conformal to g with constant T-curvature, zero Q-curvature and zero mean curvature under generic and conformally invariant assumptions. The problem amounts to solving a fourth order nonlinear elliptic boundary value problem (BVP) with boundary conditions given by a third-order pseudodifferential operator, and homogeneous Neumann one. It has a variational structure, but since the corresponding Euler-Lagrange functional is in general unbounded from below, we look for saddle points. In order to do this, we use topological arguments and min-max methods combined with a compactness result for the corresponding BVP.
  • Thumbnail Image
    Item
    Curvature flows on four manifolds with boundary
    (2007-11-12T13:22:59Z) Ndiaye, Cheikh Birahim; Mathematics; Functional Analysis and Applications
    Given a compact four dimensional smooth Riemannian manifold (M, g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero and the evolution equation by T-curvature at the boundary with the condition that the Q-curvature and the mean curvature vanish. Using integral method, we prove global existence and convergence for the Q-curvature flow (resp T-curvature flow) to smooth metric conformal to g of prescribed Q-curvature (resp T-curvature) under conformally invariant assumptions.
  • Thumbnail Image
    Item
    Multiple solutions for the scalar curvature problem on the sphere
    (2005) Ndiaye, Cheikh Birahim; Mathematics; Functional Analysis and Applications
    We study the existence of solutions for the prescribed scalar curvature problem on Sn with n ≥ 3. We prove that given an arbitrary K0 ∈ C2(Sn), K0 > 0, any positive ϵ, any α in (0, 1), and any integer l we can find such that and the equation has at least l solutions.