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math.DG2009
A rigidity theorem in Alexandrov spaces with lower curvature bound
Takumi Yokota
Distance functions of metric spaces with lower curvature bound, by definition, enjoy various metric inequalities; triangle comparison, quadruple comparison and the inequality of La…
math.DG2009
On the asymptotic reduced volume of the Ricci flow
Takumi Yokota
In this paper, 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 quantit…
math.DG2008★ 11 cited
Perelman's reduced volume and a gap theorem for the Ricci flow
Takumi Yokota
In this paper, we show that any ancient solution to the Ricci flow with the reduced volume whose asymptotic limit is sufficiently close to that of the Gaussian soliton is isometric…