Research

​Publications:
 

1. Second-order estimates for collapsed limits of Ricci-flat Kähler metrics.
(arXiv.2106.13343). Canadian Mathematics Bulletin. (here).
 

2. The Schwarz Lemma in Kähler and non-Kähler geometry. 
(arXiv.2109.06331). Asian Journal of Mathematics. (here).
 

3. The Schwarz lemma: an odyssey. 
(arXiv.2110.04989). Rocky Mountain Journal of Mathematics. (here).
 

4. On the nonnegativity of the Dirichlet energy of a weighted graph​. 
Bulletin of the Australian Mathematical Society. (here).
 

5. An eigenvalue characterization of the dual EDM cone​.
Bulletin of the Australian Mathematical Society (here).
 

6. Remarks on the quadratic orthogonal bisectional curvature. 
(​​arXiv.2211.05362). Journal of Geometry. (here).
 

7. On the weighted orthogonal Ricci curvature. 
(with Kai Tang). (arXiv.2111.00346). Journal of Geometry and Physics. (here).
 

8. On the Gauduchon curvature of Hermitian manifolds. 
(with James Stanfield). (arXiv.2211.05973). International Journal of Mathematics. (here).

​

9. (ε,𝛿)--Quasi-negative curvature and positivity of the canonical bundle. 
(with Kai Tang). (arXiv.2305.01881​​). Journal of Geometric Analysis. (here).

​

Preprints: 

​

1. Twisted Kähler--Einstein metrics and collapsing​. 
(arXiv.2003.14009)​​​​.
 

2. On Hermitian manifolds with vanishing curvature. 

(with Kai Tang). (arXiv.2201.03666).
 

3. Some remarks on the Wu--Yau theorem. 
(arXiv.2306.06509).​
​

4. A general Schwarz lemma for Hermitian manifolds. ​

(with James Stanfield). (arXiv:2309.04636). 
 

5. Hermitian metrics with vanishing second Chern Ricci curvature.

(with Artem Pulemotov). (arXiv:2309.10295).
 

In preparation:

1. Invariant metrics in complex analysis and the conjectures of Kobayashi, Lang, and Yau. 

(with Frédéric Campana and Hervé Gaussier).