6 papers
Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces
Toru Kajigaya, Keita Kunikawa
We show that the Morse index of unstable closed minimal hypersurface in a compact semi-simple Riemannian symmetric space is bounded from below by constant times the fir…
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…
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…
Convergence of mean curvature flow in hyperkähler manifolds
Keita Kunikawa, Ryosuke Takahashi
Inspired by the work of Leung-Wan, we study the mean curvature flow in hyperkähler manifolds starting from hyper-Lagrangian submanifolds, a class of middle dimensional submanifolds…
Remarks on topology of stable translating solitons
Keita Kunikawa, Shunsuke Saito
We show that any complete -stable translating soliton admits no codimension one cycle which does not disconnect . As a corollary, it follows that any two dimensional comp…