6 papers
A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation
Jianchun Chu, Man-Chun Lee, Ryosuke Takahashi
The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact Kähler manifolds that corresponds to the special Lagrangian equation in the context of the Strom…
Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow
Ryosuke Takahashi
We explore the tan-concavity of the Lagrangian phase operator for the study of the deformed Hermitian Yang-Mills (dHYM) metrics. This new property compensates for the lack of conca…
Collapsing of the line bundle mean curvature flow on Kähler surfaces
Ryosuke Takahashi
We study the line bundle mean curvature flow on Kähler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when c…
The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations
Ryosuke Takahashi
We establish a lower bound for the Donaldson-Futaki invariant of optimal degenerations produced by the Kähler-Ricci flow in terms of the greatest Ricci lower bound on arbitrary Fan…
Ricci iteration for coupled Kähler-Einstein metrics
Ryosuke Takahashi
In this paper, we introduce the "coupled Ricci iteration", a dynamical system related to the Ricci operator and twisted Kähler-Einstein metrics as an approach to the study of coupl…
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…