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Lower bound of Ricci flow's existence time
Author(s) -
Xu Guoyi
Publication year - 2015
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdv054
Subject(s) - mathematics , ricci flow , ricci curvature , scalar curvature , upper and lower bounds , curvature , flow (mathematics) , manifold (fluid mechanics) , isotropy , combinatorics , mathematical analysis , pure mathematics , geometry , physics , mechanical engineering , quantum mechanics , engineering
Let ( M n , g ) be a compact n ‐dimensional ( n ⩾ 2 ) manifold with nonnegative Ricci curvature, and if n ⩾ 3 , then we assume that ( M n , g ) × R has nonnegative isotropic curvature. The lower bound of the Ricci flow's existence time on ( M n , g ) is proved. This provides an alternative proof for the uniform lower bound of a family of closed Ricci flows' maximal existence times, which was first proved by E. Cabezas‐Rivas and B. Wilking. We also get an interior curvature estimate for n = 3 under Rc ⩾ 0 assumption among others. Combining these results, we proved the short‐time existence of the Ricci flow on a large class of three‐dimensional open manifolds, which admit some suitable exhaustion covering and have nonnegative Ricci curvature.