Xiangwen Zhang

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.

Teaching

Fall 2020:

• Math 218A - Introduction to Smooth Manifolds

Publications

• Bochner-Kodaira formulas and the Type IIA flow (with T. Fei, D.H. Phong, S. Picard), arXiv (2020)
• Geometric flows for the Type IIA string (with T. Fei, D.H. Phong, S. Picard), arXiv (2020)
• Estimates for a geometric flow for the Type IIB string (with T. Fei, D.H. Phong, S. Picard), arXiv (2020)
• 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

Links

• Analysis Seminar, Differential Geometry Seminar
• Geometry and Topology Seminar, Nonlinear PDEs, SCGAS
• Mathscinet, arXiv@Math, Gmail, Latex, Pengfei Guan, UCI Calendar, Google Calendar