14 citations · 59 across the 22 of their papers we have counts for
23 papers
New examples of Z/2 harmonic 1-forms and their deformations
Andriy Haydys, Rafe Mazzeo, Ryosuke Takahashi
We collect a number of elementary constructions of harmonic -forms, and of families of these objects. These examples show that the branching set of a harmonic…
Collapsing of -Gravitational Instantons
Yu-Shen Lin, Ryosuke Takahashi
We showed that a sequence of ALH*-gravitational instantons from pairs consisting of a weak del Pezzo surface and a smooth anti-canonical divisor towards a large complex structure l…
On the modified -equation
Ryosuke Takahashi
In this paper, we study the modified -equation introduced by Li-Shi. We first show that, on compact Kähler manifolds, the solvability of the modified -equation is equivalent…
-equation on holomorphic vector bundles
Ryosuke Takahashi
We introduce the -equation on holomorphic vector bundles over compact Kähler manifolds and investigate some fundamental properties as well as examples of solutions. In particula…
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…
Geometric quantization of coupled Kähler-Einstein metrics
Ryosuke Takahashi
We study the quantization of coupled Kähler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, so called the ``balanced metrics''.…
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…
Energy bound for Kapustin-Witten solutions on
Naichung Conan Leung, Ryosuke Takahashi
We consider solutions of Kapustin-Witten equation with Nahm pole boundary on . These solutions are usually called Nahm pole solutions. In this paper, we wil…
The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
Tristan C. Collins, Tomoyuki Hisamoto, Ryosuke Takahashi
We introduce the inverse Monge-Ampere flow as the gradient flow of the Ding energy functional on the space of Kahler metrics in for . We prove the long-time e…
Index theorem for Z/2-harmonic spinors
Ryosuke Takahashi
In my previous paper, I prove the existence of the Kuranishi structure for the moduli space of zero loci of -harmonic spinors on a 3-manifold. So a nat…
Smooth approximation of the modified conical Kähler-Ricci flow
Ryosuke Takahashi
We introduce the conical Kähler-Ricci flow modified by a holomorphic vector field. We construct a long-time solution of the modified conical Kähler-Ricci flow as the limit of a seq…
The Hessian of quantized Ding functionals and its asymptotic behavior
Ryosuke Takahashi
We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of pro…
Stability of anti-canonically balanced metrics
Shunsuke Saito, Ryosuke Takahashi
We study the asymptotic behavior of quantized Ding functionals along Bergman geodesic rays and prove that the slope at infinity can be expressed in terms of Donaldson-Futaki invari…
Bergman iteration and -convergence towards Kähler-Ricci flow
Ryosuke Takahashi
On a polarized manifold , the Bergman iteration is defined as a sequence of Bergman metrics on with two integer parameters . We study the relation betw…
Asymptotic stability for Kähler-Ricci solitons
Ryosuke Takahashi
We show that the coercivity of the modified Ding functional leads to the existence of a certain kind of balanced metrics and their convergence to the Kähler-Ricci soliton modulo au…
The moduli space of -type zero loci for -harmonic spinors in dimension 3
Ryosuke Takahashi
Let be a compact oriented 3-dimensional smooth manifold. In this paper, we construct a moduli space consisting of pairs where is a -embedding simple closed cu…
On the modified Futaki invariant of complete intersections in projective spaces
Ryosuke Takahashi
It is known that a necessary condition for the existence of Kähler-Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian-Zhu. In a recent work of Berm…
Modified Kähler-Ricci flow on projective bundles
Ryosuke Takahashi
In this paper, we propose a method of studying the modified Kahler-Ricci flow on projective bundles and give the explicit equation from the view point of symplectic geometry.
An Ancient Solution of The Ricci Flow in Dimension 4 Converging to the Euclidean Schwarzschild Metric
Ryosuke Takahashi
In this paper, we prove the existence of an ancient solution to the Ricci flow whose limit at is the Euclidean Schwarzschild metric.