TY - JOUR
T1 - Bounding scalar curvature for global solutions of the Kähler-Ricci flow
AU - Song, Jian
AU - Tian, Gang
N1 - Publisher Copyright:
© 2016 by Johns Hopkins University Press.
PY - 2016/6
Y1 - 2016/6
N2 - We show that the scalar curvature is uniformly bounded for the normalized Kähler-Ricci flow on a Kähler manifold with semi-ample canonical bundle. In particular, the normalized Kähler- Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kähler surfaces, projective manifolds of complex dimension three, and for projective manifolds of all dimensions if assuming the abundance conjecture.
AB - We show that the scalar curvature is uniformly bounded for the normalized Kähler-Ricci flow on a Kähler manifold with semi-ample canonical bundle. In particular, the normalized Kähler- Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kähler surfaces, projective manifolds of complex dimension three, and for projective manifolds of all dimensions if assuming the abundance conjecture.
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U2 - 10.1353/ajm.2016.0025
DO - 10.1353/ajm.2016.0025
M3 - Article
AN - SCOPUS:84970021037
SN - 0002-9327
VL - 138
SP - 683
EP - 695
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 3
ER -