4 papers · 1 filter
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…
Hamilton type entropy formula along the Ricci flow on surfaces with boundary
Keita Kunikawa, Yohei Sakurai
In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy fun…
On Ecker's local integral quantity at infinity for ancient mean curvature flows
Keita Kunikawa
We point out that Ecker's local integral quantity agrees with Huisken's global integral quantity at infinity for ancient mean curvature flows if Huisken's one is finite on each tim…
Liouville theorem for heat equation along ancient super Ricci flow via reduced geometry
Keita Kunikawa, Yohei Sakurai
The aim of this article is to provide a Liouville theorem for heat equation along ancient super Ricci flow. We formulate such a Liouville theorem under a growth condition concernin…