Associate Professor

Department of Mathematics

University of California, Irvine

510D Rowland Hall

Irvine, CA 92697-3875

Phone: (949) 824-3156

Email: xiangwen@math.uci.edu

My research interests are geometric analysis and partial differential equations. Here is my CV.

Fall 2019:

- Math 205A - Introduction to Graduate Analysis

*Parabolic complex Monge-Ampere equations on compact Kahler manifolds*(with S. Picard), arXiv (2019)*On a class of curvature equations*(with P. Guan), Pure Appl. Math. Q., accepted (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