TY - JOUR
T1 - Blow-up rate of the scalar curvature along the conical Kähler–Ricci flow with finite time singularities
AU - Nomura, Ryosuke
N1 - Funding Information:
The author would like to express his gratitude to his supervisor Prof. Shigeharu Takayama for various comments. This work is supported by the Program for Leading Graduate Schools, MEXT , Japan.
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/6
Y1 - 2018/6
N2 - We investigate the scalar curvature behavior along the normalized conical Kähler–Ricci flow ωt, which is the conic version of the normalized Kähler–Ricci flow, with finite maximal existence time T<∞. We prove that the scalar curvature of ωt is bounded from above by C/(T−t)2 under the existence of a contraction associated to the limiting cohomology class [ωT]. This generalizes Zhang's work to the conic case.
AB - We investigate the scalar curvature behavior along the normalized conical Kähler–Ricci flow ωt, which is the conic version of the normalized Kähler–Ricci flow, with finite maximal existence time T<∞. We prove that the scalar curvature of ωt is bounded from above by C/(T−t)2 under the existence of a contraction associated to the limiting cohomology class [ωT]. This generalizes Zhang's work to the conic case.
KW - Cone metric
KW - Conical Kähler–Ricci flow
KW - Monge–Ampère equation
KW - Scalar curvature
KW - Twisted Kähler–Ricci flow
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U2 - 10.1016/j.difgeo.2017.12.001
DO - 10.1016/j.difgeo.2017.12.001
M3 - Article
AN - SCOPUS:85040645862
VL - 58
SP - 1
EP - 16
JO - Differential Geometry and its Applications
JF - Differential Geometry and its Applications
SN - 0926-2245
ER -