TY - JOUR
T1 - On the equivalence between noncollapsing and bounded entropy for ancient solutions to the Ricci flow
AU - Zhang, Yongjia
N1 - Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - As a continuation of a previous paper, we prove Perelman's assertion, that is, for ancient solutions to the Ricci flow with bounded nonnegative curvature operator, uniformly bounded entropy is equivalent to κ-noncollapsing on all scales. We also establish an equality between the asymptotic entropy and the asymptotic reduced volume, which is a result similar to a paper by Xu (2017), where he assumes the Type I curvature bound.
AB - As a continuation of a previous paper, we prove Perelman's assertion, that is, for ancient solutions to the Ricci flow with bounded nonnegative curvature operator, uniformly bounded entropy is equivalent to κ-noncollapsing on all scales. We also establish an equality between the asymptotic entropy and the asymptotic reduced volume, which is a result similar to a paper by Xu (2017), where he assumes the Type I curvature bound.
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U2 - 10.1515/crelle-2018-0022
DO - 10.1515/crelle-2018-0022
M3 - Article
AN - SCOPUS:85056147600
SN - 0075-4102
VL - 2020
SP - 35
EP - 51
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 762
ER -