TY - JOUR
T1 - On the asymptotic reduced volume of the Ricci flow
AU - Yokota, Takumi
N1 - Funding Information:
Acknowledgments The author would like to express his gratitude to his adviser Takao Yamaguchi for his encouragement. This work was supported in part by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2010/3
Y1 - 2010/3
N2 - In this article, we consider two different monotone quantities defined for the Ricci flow and show that their asymptotic limits coincide for any ancient solutions. One of the quantities we consider here is Perelman's reduced volume, while the other is the local quantity discovered by Ecker, Knopf, Ni, and Topping. This establishes a relation between these two monotone quantities.
AB - In this article, we consider two different monotone quantities defined for the Ricci flow and show that their asymptotic limits coincide for any ancient solutions. One of the quantities we consider here is Perelman's reduced volume, while the other is the local quantity discovered by Ecker, Knopf, Ni, and Topping. This establishes a relation between these two monotone quantities.
KW - Ancient solution
KW - Monotonicity formula
KW - Reduced volume
KW - Ricci flow
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U2 - 10.1007/s10455-009-9184-6
DO - 10.1007/s10455-009-9184-6
M3 - Article
AN - SCOPUS:77951204458
VL - 37
SP - 263
EP - 274
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
SN - 0232-704X
IS - 3
ER -