Listed in reverse chronological order.
The Miyaoka-Yau inequality and the delta invariant for Fano varieties.
This is a joint work with M. Iwai.
arXiv
Continuity method for the Mabuchi soliton on the extremal Fano manifold.
This is a joint work with S. Nakamura.
arXiv To appear in Ann. Inst. Fourier.
On the Miyaoka-Yau inequality for manifolds with nef anti-canonical line bundle.
This is suspended, because the proof of the main theorem fails.
arXiv
Quantization of the Kähler-Ricci flow and Optimal destabilizer for a Fano manifold.
arXiv Ann. Glob. Anal. Geom., 69 (2026).
Mabuchi's soliton metric and relative D-stability.
arXiv Am. J. Math., 145 (2023), 765--806.
Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold.
arXiv The Journal of Geometric Analysis 33 (2023).
The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics.
This is a joint work with T. C. Collins and R. Takahashi.
arXiv Jour. Differential Goemetry 120 (2022), 51-95.
Stability and coercivity for toric polarizations.
arXiv To appear in Kodai Math. J.
Orthogonal projection of a test configuration to vector fields.
arXiv
Uniform K-stability and asymptotics of energy functionals in Kähler geometry.
This is a joint work with S. Boucksom and M. Jonsson.
arXiv J. Eur. Math. Soc. 21 no.9 (2019), 2905-2944.
Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs.
This is a joint work with S. Boucksom and M. Jonsson.
arXiv Ann. Inst. Fourier (Grenoble) 67 no. 2 (2017), 743-841.
On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold.
arXiv J. Reine Angew. Math. 713 (2016), 129--148.
On the volume of graded linear series and Monge Ampère mass.
arXiv Math. Z. 275 (2013), 233--243.
Remarks on $L^2$-jet extension and extension of singular Hermitian metric with semipositive curvature.
arXiv
Restricted Bergman kernel asymptotics.
arXiv Trans. Amer. Math. Soc. 364 (2012), 3585-3607.