60 citations · 196 across the 34 of their papers we have counts for
35 papers
On weighted extremal Kähler metrics
Akito Futaki
The notion of weighted extremal Kähler metrics extends the classical notion of Calabi's extremal Kähler metrics, but includes many well-studied objects in Kähler geometry such as K…
On coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds
Akito Futaki
We consider coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds. These are natural generalizations of Kähler-Einstein metrics. As in the case of Kähler-Einstein…
An asymptotic slope of the α-K-energy for the Kahler-Yang-Mills equations
Akito Futaki, Jianwei Shi
For holomorphic vector bundles over compact Kähler manifolds, we establish a formula for the asymptotic slope of the α-K-energy associated with the Kahler-Yang-Mills equations.
Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory
Tobias Diez, Akito Futaki, Tudor Ratiu
We pioneer the development of a rigorous infinite-dimensional framework for the Kempf-Ness theorem, addressing the significant challenge posed by the absence of a complexification…
Deformations of Fano manifolds with weighted solitons
Akito Futaki
We consider weighted solitons on Fano manifolds which include Kaehler-Ricci solitons, Mabuchi solitons and base metrics which induce Calabi-Yau cone metrics outside the zero sectio…
Hodge Laplacian and geometry of Kuranishi family of Fano manifolds
Akito Futaki, Xiaofeng Sun, Yingying Zhang
We first obtain eigenvalue estimates for the Hodge Laplacian on Fano manifolds, which follow from the Bochner-Kodaira formula. Then we apply it to study the geometry of the Kuranis…