TY - JOUR
T1 - New differential operator and noncollapsed rcd spaces
AU - Honda, Shouhei
N1 - Publisher Copyright:
© 2020, Mathematical Science Publishers. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We show characterizations of noncollapsed compact RCD(K; N ) 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 L2 via the heat kernel. This seems to be the first application of geometric flow to the study of RCD spaces.
AB - We show characterizations of noncollapsed compact RCD(K; N ) 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 L2 via the heat kernel. This seems to be the first application of geometric flow to the study of RCD spaces.
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U2 - 10.2140/gt.2020.24.2127
DO - 10.2140/gt.2020.24.2127
M3 - Article
AN - SCOPUS:85096667584
VL - 24
SP - 2127
EP - 2148
JO - Geometry and Topology
JF - Geometry and Topology
SN - 1465-3060
IS - 4
ER -