TY - JOUR
T1 - The complex monge-ampère equation on some compact hermitian manifolds
AU - Chu, Jianchun
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015
Y1 - 2015
N2 - We consider the complex Monge-Ampère equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W1,q0 for any q0 > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W3,q0 for the complex Monge-Ampère equation when F is in W1,q0.
AB - We consider the complex Monge-Ampère equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W1,q0 for any q0 > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W3,q0 for the complex Monge-Ampère equation when F is in W1,q0.
KW - Compact hermitian manifold
KW - Complex monge-ampère equation
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U2 - 10.2140/pjm.2015.276.369
DO - 10.2140/pjm.2015.276.369
M3 - Article
AN - SCOPUS:84938277211
VL - 276
SP - 369
EP - 386
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
SN - 0030-8730
IS - 2
ER -