Research

Listed in reverse chronological order. 

• Quantization of the Kähler-Ricci flow and Optimal destabilizer for a Fano manifold. 

• Mabuchi's soliton metric and relative D-stability. To appear in American Journal of Mathematics.  
  arXiv 

• Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold.  The Journal of Geometric Analysis 33 (2023).
  arXiv 

• The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics. Jour. Differential Goemetry 120 (2022), 51-95.   
  This is a joint work with T. C. Collins and R. Takahashi.
  arXiv 

• Stability and coercivity for toric polarizations.
  arXiv 

• Orthogonal projection of a test configuration to vector fields.
  arXiv 

• Uniform K-stability and asymptotics of energy functionals in Kähler geometry. J. Eur. Math. Soc. 21 no.9 (2019), 2905-2944. 
  This is a joint work with S. Boucksom and M. Jonsson.
  arXiv 

• Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs. Ann. Inst. Fourier (Grenoble) 67 no. 2 (2017), 743-841.
  This is a joint work with S. Boucksom and M. Jonsson.
  arXiv 

• On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold. J. Reine Angew. Math. 713 (2016), 129--148.
  Journal  arXiv

• On the volume of graded linear series and Monge Ampère mass. Math. Z. 275 (2013), 233--243.
  Journal  arXiv

• Remarks on $L^2$-jet extension and extension of singular Hermitian metric with semipositive curvature.
  arXiv

• Restricted Bergman kernel asymptotics. Trans. Amer. Math. Soc. 364 (2012), 3585-3607.
  Journal  arXiv