Xiangwen Zhang
Professor, Mathematics
School of Physical Sciences
School of Physical Sciences
Ph.D., McGill University, 2012
B.S., University of Science and Technology of China, 2007
B.S., University of Science and Technology of China, 2007
University of California, Irvine
510D Rowland Hall
Mail Code: 3875
Irvine, CA 92697
510D Rowland Hall
Mail Code: 3875
Irvine, CA 92697
Research Interests
Differential Geometry, Partial Differential Equations
Websites
Publications
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
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 Societies
American Mathematical Society
Link to this profile
https://faculty.uci.edu/profile/?facultyId=6586
https://faculty.uci.edu/profile/?facultyId=6586
Last updated
07/02/2023
07/02/2023