I am a geometric analyst with a concentration of research on complex differential geometry. All my papers can be found in preprint form on the arXiv. I am also present on Google Scholar.

SURVEY PAPERS:

Relative pluripotential theory on compact Kähler manifolds, with E. Di Nezza, C. H. Lu, preprint, to appear in Pure. Appl. Math. Q. 21 (2025), no. 3, pp. 1037-1118. arXiv:2303.11584

Geometric pluripotential theory on Kähler manifolds, Advances in complex geometry, 1-104, Contemp. Math. 735, Amer. Math. Soc., Providence, RI, 2019, arXiv:1902.01982

RESEARCH PAPERS:

The trace operator of quasi-plurisubharmonic functions on compact Kähler manifolds, with M. Xia, preprint, arXiv:2403.08259

Transcendental Okounkov bodies, with R. Reboulet, M. Xia, D. Witt Nystrom, K. Zhang, preprint, arXiv:2309.07584

A transcendental approach to non-Archimedean metrics of pseudoeffective classes, with M. Xia, K. Zhang, preprint, to appear in Comment. Math. Helv. arXiv:2302.02541

Twisted Kähler-Einstein metrics in big classes, with K. Zhang, Comm. Pure Appl. Math. 77 (2024), no. 12, 4289--4327. arXiv:2208.08324

The volume of pseudoeffective line bundles and partial equilibrium, with M. Xia, Geom. and Topol. 28-4 (2024), 1957--1993 arXiv:2112.03827

The Mabuchi geometry of low energy classes, Math. Ann. 389 (2024), no. 1, 427--450. arXiv:2109.11581

The closures of test configurations and algebraic singularity types, with M. Xia, Adv. Math. 397 (2022), Paper No. 108198. arXiv:2003.04818

Griffiths extremality, interpolation of norms, and Kähler quantization, with K.-R. Wu, J. Geom. Anal. 32 (2022), no. 7, Paper No. 203. arXiv:1910.01782

The metric geometry of singularity types, with E. Di Nezza and C.H. Lu, J. Reine Angew. Math. 771 (2021), 137-170. arXiv:1909.00839

The isometries of the space of Kähler metrics, J. Eur. Math. Soc. 23 (2021), no. 12, 4091--4108. arXiv:1902.06124

Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry, with C.H. Lu, Geom. and Topol. 24 (2020), no. 4, 1907-1967 arXiv:1810.04661

Quantization in geometric pluripotential theory, with C.H. Lu and Y.A. Rubinstein, Comm. Pure Appl. Math. 73 (2020), no. 5, 1100-1138 arXiv:1809.03800

Log-concavity of volume and complex Monge-Ampere equations with prescribed singularity, with E. Di Nezza and C.H. Lu, Math. Ann. 379 (2021), no. 1-2, 95-132. arXiv:1807.00276

L^1 metric geometry of big cohomology classes, with E. Di Nezza and C.H. Lu, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 7, 3053-3086. arXiv:1802.00087

Compactness of Kähler metrics with bounds on Ricci curvature and I functional, with X.X. Chen and W. He, Calc. Var. PDE 58 (2019), no. 4, Paper No. 139. arXiv:1712.05095

Convergence of the Kähler-Ricci iteration, with Y.A. Rubinstein, Analysis & PDE 12 (2019), no. 3. 721-735. arXiv:1705.06253

Monotonicity of non-pluripolar products and complex Monge-Ampere equations with prescribed singularity, with E. Di Nezza and C.H. Lu, Analysis & PDE 11 (2018), no. 8. arXiv:1705.05796

A minimum principle for Lagrangian graphs, with Y.A. Rubinstein, Comm. Anal. Geom. 27 (2019), no. 4, 857-876. arXiv:1606.08818

On the singularity type of full mass currents in big cohomology classes, with E. Di Nezza and C.H. Lu, Compos. Math. 154 (2018), no. 2, 380-409. arXiv:1606.01527

Regularity of weak minimizers of the K-energy and applications to properness and K-stability, with R. Berman and C.H. Lu, Ann. Sci. Ec. Norm. Super. 53 (2020), no. 4, 267-289, arXiv:1606.03114

Metric geometry of normal Kähler spaces, energy properness, and existence of canonical metrics, IMRN (2017), no. 22, 6752-6777. arXiv:1604.07127

Comparison of the Calabi and Mabuchi geometries and applications to geometric flows, Ann. Inst. H. Poincare Anal. Non Lineaire 34 (2017), no. 5, 1131-1140. arXiv:1602.04309

Convexity of the extended K-energy and the long time behavior of the Calabi flow, with R.J. Berman and C.H. Lu, Geom. and Topol. 21 (2017), no. 5, 2945-2988. arXiv:1510.01260

Tian's properness conjectures and Finsler geometry of the space of Kähler metrics, with Y.A. Rubinstein, J. Amer. Math. Soc. 30 (2017), no. 2, 347-387. arXiv:1506.07129

Geodesic rays and Kähler-Ricci trajectories on Fano manifolds, with W. He, Trans. Amer. Math. Soc. 369 (2017), no. 7, 5069-5085. arXiv:1411.0774

The Mabuchi geometry of finite energy classes, Adv. Math. 285 (2015), 182-219. arXiv:1409.2072

Kiselman's principle, the Dirichlet problem for the Monge-Ampere equation, and rooftop obstacle problems, with Y.A. Rubinstein, J. Math. Soc. Japan 68 (2016), no. 2, 773-796. arXiv:1405.6548

The Mabuchi completion of the space of Kähler potentials, Amer. J. Math. 139 (2017), no. 5, 1275-1313. arXiv:1401.7318

Weak geodesic rays in the space of Kähler potentials and the class E(X,ω), J. Inst. Math. Jussieu 16 (2017), no. 4, 837-858. arXiv:1307.6822

Morse theory and geodesics in the space of Kähler metrics, Proc. Amer. Math. Soc. 142 (2014), no. 8, 2775-2782. arXiv:1207.4465

Weak geodesics in the space of Kähler metrics, with L. Lempert, Math. Res. Lett. 19 (2012), no. 5, 1127-1135. arXiv:1205.0840

RESEARCH PAPERS WITH UNDERGRADUATES:

The Hausdorff distance and metrics on toric singularity types, with A. Aitokhuehi, B. Braiman, D. Cutler, R. Deaton, P. Gupta, J. Horsley, V. Pidaparthy, J. Tang, preprint, arXiv:2411.11246

Extremizers of the J functional with respect to the d_1 metric, with S. Bachhuber, A. Benda, B. Christophel, Analysis Math. 48 (2022), no. 2, 307-330. arXiv:2304.06323

Optimal asymptotic of the J functional with respect to the d_1 metric, with E. George and K. Smith, Selecta Math. (N.S.) 28 (2022), no. 2, Paper No. 43. arXiv:2101.02589