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SPACE OF RICCI FLOWS (II)—PART A: MODULI OF SINGULAR CALABI–YAU SPACES

Part of: Global differential geometry

Published online by Cambridge University Press:  28 December 2017

XIUXIONG CHEN  and
BING WANG
XIUXIONG CHEN
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA School of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China; xiu@math.sunysb.edu
BING WANG
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA; bwang@math.wisc.edu

Abstract

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We establish the compactness of the moduli space of noncollapsed Calabi–Yau spaces with mild singularities. Based on this compactness result, we develop a new approach to study the weak compactness of Riemannian manifolds.

MSC classification

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 5 , 2017 , e32
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2017

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