Connectedness at infinity of complete Kähler manifolds

• Autores: Peter Li, Jiaping Wang
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 131, Nº 3, 2009, págs. 771-817
• Idioma: inglés
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• Resumen

  • One of the main purposes of this paper is to prove that on a complete K\"ahler manifold of dimension $m$, if the holomorphic bisectional curvature is bounded from below by -1 and the minimum spectrum $\lambda_1(M) \ge m^2$, then it must either be connected at infinity or isometric to ${\Bbb R} \times N$ with a specialized metric, with $N$ being compact. Generalizations to complete K\"ahler manifolds satisfying a weighted Poincar\'e inequality are also being considered.