2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65768In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. We prove that a complete noncompact Kähler surface with positive and bounded sectional curvature and with finite analytic Chern number $c_{1}(M)^{2}$ is biholomorphic to ${\C}^2$.33 pagesDifferential Geometrytext