Publications

1995

• On a variational problem with lack of compactness: the topological effect of the critical points at infinity
  
  • Bahri Abbas
  • Li Yanyan
  • Rey Olivier
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 1995, 3, pp.67-94. We study the subcritical problems (P_ɛ) : −Δu = u^(p−ɛ), u>0 on Ω, u=0 on ∂Ω, Ω being a smooth and bounded domain in ℝ^N, N≥3, p+1=2N/N−2 the critical Sobolev exponent and ɛ>0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P_0).
• La première valeur propre de l'opérateur de Dirac sur les variétés kählériennes compactes
  
  • Moroianu Andrei
  Communications in Mathematical Physics, Springer Verlag, 1995, 169, pp.373-384. K.D. Kirchberg gave a lower bound for the first eigenvalue of the Dirac operator on a spin compact Kähler manifoldM of odd complex dimension with positive scalar curvature. We prove that manifolds of real dimension 8l+6 satisfying the limiting case are twistor space of quaternionic Kähler manifold with positive scalar curvature and that the only manifold of real dimension 8l+2 satisfying the limiting case is the complex projective space CP^{4l+1}. (10.1007/BF02099477)
  DOI : 10.1007/BF02099477