27 citations · 29 across the 3 of their papers we have counts for
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Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry
Keita Kunikawa, Yohei Sakurai
We study harmonic map heat flow along ancient super Ricci flow, and derive several Liouville theorems with controlled growth from Perelman's reduced geometric viewpoint. For non-po…
Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition
Keita Kunikawa, Yohei Sakurai
In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Und…
Comparison geometry of manifolds with boundary under lower -weighted Ricci curvature bounds with -range
Kazuhiro Kuwae, Yohei Sakurai
We study comparison geometry of manifolds with boundary under a lower -weighted Ricci curvature bound for with -range introduced…
Maximal diameter theorem for directed graphs of positive Ricci curvature
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
In a previous work, the authors have introduced a Lin-Lu-Yau type Ricci curvature for directed graphs, and obtained a diameter comparison of Bonnet-Myers type. In this paper, we in…
Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
For undirected graphs, the Ricci curvature introduced by Lin-Lu-Yau has been widely studied from various perspectives, especially geometric analysis. In the present paper, we discu…
Upper bounds for higher-order Poincar'e constants
Kei Funano, Yohei Sakurai
We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of…