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New
differential operator and noncollapsed $\mathrm{RCD}$
spaces
Shouhei Honda |
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Geometry & Topology 24 (2020) 2127–2148
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Abstract |
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We show characterizations of noncollapsed compact spaces, which in particular confirm a conjecture of De Philippis and Gigli on the implication from the weakly noncollapsed condition to the noncollapsed one in the compact case. The key idea is to give the explicit formula of the Laplacian associated to the pullback Riemannian metric by embedding in via the heat kernel. This seems to be the first application of geometric flow to the study of spaces. |
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Dedicated to Professor Kenji Fukaya on his 60th birthday |
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Keywords
Ricci curvature, Laplacian, metric measure space
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Mathematical Subject Classification 2010
Primary: 53C21
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References |
Publication
Received: 28 June 2019
Revised: 18 August 2019
Accepted: 23 September 2019
Published: 10 November 2020
Proposed: Tobias H Colding
Seconded: Gang Tian, Bruce Kleiner
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Authors |
| Shouhei Honda | |
| Mathematical Institute Tohoku University Sendai Japan |
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