Xiangwen Zhang

Associate Professor, Mathematics
School of Physical Sciences

Ph.D., McGill University, 2012
M.S., McGill University, 2008
B.S., University of Science and Technology of China, 2007

Phone: (949) 824-3156
Email: xiangwen@uci.edu

University of California, Irvine
510D Rowland Hall
Mail Code: 3875
Irvine, CA 92697
Research Interests
Differential Geometry, Partial Differential Equations
2019-Now: Associate Professor, Department of Mathematics, UC Irvine.
2015-2019: Assistant Professor, Department of Mathematics, UC Irvine.
2012-2015: Ritt Assistant Professor, Department of Mathematics, Columbia University.
Parabolic complex Monge-Ampere equations on compact Kahler manifolds (with S. Picard), arXiv (2019)

A flow of conformally balanced metrics with Kahler fixed points (with D.H. Phong, S. Picard), arXiv, Math. Ann., accepted (2019)

Regularity of degenerate Hessian equation (with S. Dinew, S. Plis), arXiv, Calculus of Variations and PDE, accepted (2019)

The Anomaly flow on unimodular Lie groups (with D.H. Phong, S. Picard), arXiv, Contemp. Math., accepted (2018).

Fu-Yau Hessian Equation (with D.H. Phong, S. Picard), arXiv, Journal of Differential Geometry, accepted (2018)

A rigidity theorem for surfaces in Schwarzschild manifold (with P.-N. Chen), arXiv, International Mathematics Research Notices, accepted (2018)

The Anomaly flow and the Fu-Yau equation (with D.H. Phong, S. Picard), arXiv, Annals of PDE, Vol.4, Issue 2, (2018)

Anomaly flows (with D.H. Phong, S. Picard), arXiv, Comm. Anal. Geom., Vol. 26, No. 4 (2018), 955-1008

Geometric flows and Strominger systems (with D.H. Phong, S. Picard), Mathematische Zeitschrift, (2018) Vol. 288, 101–113

New curvature flows in complex geometry (with D.H. Phong, S. Picard), arXiv, Surveys in Differential Geometry, Vol. 22, No. 1 (2017), 331-364

The Fu-Yau equation with negative slope parameter (with D.H. Phong, S. Picard), Inventiones Mathematicae, Vol. 209, No. 2 (2017), 541-576

Minkowski formulae and Alexandrov theorems in spacetimes (with M.T. Wang, Y.K. Wang), Journal of Differential Geometry, Vol. 105, No. 2 (2017), 249-290

ABP estimate and Geometric inequalities (with C. Xia), Comm. Anal. Geom., Vol. 25, No. 3 (2017), 685-708

On estimates for the Fu-Yau generalization of a Strominger system (with D.H. Phong, S. Picard), J. Reine Angew. Math. (Crelle’s Journal), Vol. 2019, Issue 751 (2019), 243-274

A second order estimate for general complex Hessian equations (with D.H. Phong, S. Picard), Analysis and PDE, 9 (2016), No. 7, 1693-1709

A proof of the Alexandrov’s uniqueness theorem for convex surfaces in R^3 (with P. Guan, Z. Wang), Ann. Inst. H. Poincaré Anal. Non-Linéaire, 33 (2016), 329-336

Generalized Kahler-Einstein metrics and Energy functionals (with X. Zhang), Canadian Journal of Mathematics, 66 (2014), 1413-1435

Alexandrov-Bakelman-Pucci estimate on Riemannian manifolds (with Y. Wang), Advance in Mathematics, 232 (2013), Issue 1, 499-512

On the boundary of Kahler cone, Proc. Amer. Math. Soc., 140 (2012), 701-705

Measure estimates, Harnack inequalities and Ricci lower bound (with Y. Wang), arXiv: 1102.5567, Universitatis Iagellonicae Acta Mathematics, accepted (2018)

Regularity estimates for the complex Monge-Ampere equations on Hermitian manifolds (with X. Zhang), Journal of Functional Analysis, Vol 260, Issue 7, (2011), 2004-2026

The C^{2, \alpha} estimate of complex Monge-Ampere equation (with S. Dinew, X. Zhang), Indiana Univ. Math. J., 60 (2011), 1713-1722

A priori estimate for complex Monge Ampere equations on Hermitian manifolds, International Mathematics Research Notices, Vol 2010, Issue 19, (2010), 3814-3836

Mean curvature flow for Lagrangian submanifolds with convex potentials, Master Thesis, McGill University, 2008
Professional Society
American Mathematical Society
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