7 citations · 11 across the 11 of their papers we have counts for
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Counterexamples to preservation of flat normal bundles under mean curvature flow
Keita Kunikawa
We construct an embedded torus and an entire graph in whose normal bundles are initially flat but lose this property instantaneously under mean curvature flow. We al…
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…
Almost splitting and quantitative stratification for super Ricci flow
Keita Kunikawa, Yohei Sakurai
The aim of this paper is to study almost rigidity properties of super Ricci flow whose Muller quantity is non-negative. We conclude almost splitting and quantitative stratification…
Gaussian heat kernel estimates of Bamler-Zhang type along super Ricci flow
Keita Kunikawa, Yohei Sakurai
Bamler-Zhang have developed geometric analysis on Ricci flow with scalar curvature bound. The aim of this paper is to extend their work to various geometric flows. We generalize so…
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…
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…
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…
Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow
Toru Kajigaya, Keita Kunikawa
In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kähler-Einstein manifold to more general Kähl…
Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature
Keita Kunikawa
In this paper, we derive a mean curvature estimate for eternal solutions (including translating solutions) of almost-calibrated Lagrangian mean curvature flow in complex Euclidean…