Geometric Analysis; Affine and Projective Geometric Structures; Teichmüller Theory; Affine Differential Geometry
- Coordinates on the Augmented Moduli Space of Convex RP2 Structures (with Tengren Zhang), preprint, 2018, to appear, Journal of the London Mathematical Society.
- The Moduli Spaces of Equivariant Minimal Surfaces in RH3 and RH4 via Higgs Bundles (with Ian McIntosh), Geometriae Dedicata, 2019.
- Equivariant Minimal Surfaces in CH2 and Their Higgs Bundles (with Ian McIntosh), Asian Journal of Mathematics, 2019.
- Convex RP2 Structures and Cubic Differentials Under Neck Separation, Journal of Differential Geometry, 2019.
- Approximate Yang-Mills-Higgs Metrics on Flat Higgs Bundles over an Affine Manifold (with Indranil Biswas and Matthias Stemmler), Communications in Analysis and Geometry, 2014.
- The Vortex Equations on Affine Manifolds (with Indranil Biswas and Matthias Stemmler), Transactions of the AMS, 2014.
- Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH2 (with Zheng Huang and Marcello Lucia), Mathematical Research Letters, 2013.
- Affine Yang-Mills-Higgs Metrics (with Indranil Biswas and Matthias Stemmler), Journal of Symplectic Geometry, 2013.
- Minimal Lagrangian Surfaces in CH2 and Representations of Surface Groups into SU(2,1) (with Ian McIntosh), Geometriae Dedicata, 2013.
- Hermitian-Einstein Connections on Principal Bundles over Flat Affine Manifolds (with Indranil Biswas), International Journal of Mathematics, 2012.
- Affine Hermitian-Einstein Metrics, Asian Journal of Mathematics, 2009.
- Limits of Solutions to a Parabolic Monge Ampère Equation (with Mao-Pei Tsui), in Proceeding of the International Conference on Geometric Analysis, NCTS (Taipei, Taiwan; June, 2007), 2009.
- Ancient Solutions of the Affine Normal Flow (with Mao-Pei Tsui), Journal of Differential Geometry, 2008.
- Flat Metrics, Cubic Differentials and Limits of Projective Holonomies, Geometriae Dedicata, 2007.
- Affine Manifolds, SYZ Geometry and the “Y” Vertex (with Shing-Tung Yau and Eric Zaslow), Journal of Differential Geometry, 2005, with erratum, 2008.
- Singular Semi-Flat Calabi-Yau Metrics on S2, Communications in Analysis and Geometry, 2005.
- The Compactification of the Moduli Space of Convex RP2 Surfaces, I, Journal of Differential Geometry, 2004.
- Affine Spheres and Kähler-Einstein Metrics, Mathematical Research Letters, 2002.
- Riemannian Metrics on Locally Projectively Flat Manifolds, American Journal of Mathematics, 2002.
- Affine Spheres and Convex RPn Manifolds, American Journal of Mathematics, 2001.
- Dissertation, Harvard University, 1999.
- On the Donaldson-Uhlenbeck-Yau Correspondence, Notices of the International Congress of Chinese Mathematicians, 2019.
- Cubic Differentials in the Differential Geometry of Surfaces (with Ian McIntosh), in Handbook of Teichmüller Theory (Vol. 6), 2016.
- Flat Bundles on Affine Manifolds (with Indranil Biswas and Matthias Stemmler), Arabian Journal of Mathematics, 2013.
- Cheng and Yau’s Work on the Monge-Ampère Equation and Affine Geometry (with Xu-Jia Wang and Deane Yang), in Geometry and Analysis (Vol. I), 2010.
- Survey on Affine Spheres, in Handbook of Geometric Analysis (Vol. II), 2010.