On partial uniqueness of complete non-compact Ricci flat metrics

Abstract

Using techniques for Caccioppoli inequality, on a fairly general class of complete non-compact Kähler manifolds with sub-quadratic volume growth, we show uniqueness of bounded $C^{1,1}$ solution to Monge-Ampere equation. This does not a priori require any decay of the solution.

References are added. Presentation is improved. The proof of Corollary 1.3 SOB(2)-case is revised. More explanations are added. 8 pages