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Space of Ricci Flows I
Author(s) -
Chen Xiuxiong,
Wang Bing
Publication year - 2012
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21414
Subject(s) - mathematics , scalar curvature , ricci flow , compact space , isoperimetric inequality , bounded function , compactness theorem , moduli space , mathematical analysis , pure mathematics , ricci curvature , moduli , curvature , geometry , fixed point theorem , brouwer fixed point theorem , physics , quantum mechanics
In this paper, we study the moduli spaces of m ‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient shrinking solitons. © 2012 Wiley Periodicals, Inc.
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