Prescribing the Ricci curvature of Kähler asymptotically Cn manifolds, n > 2

✍ Scribed by Philippe Delanoë

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 626 KB
• Volume: 4
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/0926-2245(94)00009-3

✦ Synopsis

An analogue of Calabi's conjecture was posed on a class of complete noncompact Kihler manifolds [5], then solved on the simplest of them, the complex n-space with n > 2 [9]. Here we prove the conjecture in its full generality, by inverting an elliptic complex Monge-Amp&e operator between suitable FrCchet spaces of smooth functions vanishing at infinity. A priori estimates benefit from recent simplifications of [2]. I(eywords: Ricci, Kkhler, complex Monge-Ampke, complete noncompact, asymptotic behavior, a priori estimates.