Some of My Publications

Published Papers

P. Guan and X. Zhang, Regularity of the geodesic equation in the space of Sasakian metrics
Advances in Mathematics, Volume 230, (2012) 321-371.

P. Guan, J. Li and Y.Y. Li, Hypersurfaces of prescribed curvature measures,
Duke Math. J. Vol. 161, No. 10 (2012), 1927-1942.

P. Guan and L. Xu, Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations.
to appear in Journal fur die reine und angewandte Mathematik.DOI 10.1515/crelle.2012.038

P. Guan and D. Phong, A maximum rank problem for degenerate elliptic fully nonlinear equations.
to appear in Math. Ann., DOI 10.1007/s00208-011-0729-1

P. Guan and D. Phong, Partial Legendre transforms of nonlinear equations.
to appear in Proc. AMS. S 0002-9939(2012)11210-9

B. Bian, P. Guan, X. Ma and L. Xu, A constant rank theorem for quasiconcave solutions of fully nonlinear partial differential equations.
to appear in Indiana University Mathematics Journal, Vol. 60, (2011) 101-120.

P. Guan and X. Zhang, A Geodesic equation in the space of Sasakian metrics
Geometry and Analysis I, pp. 303-318. Ed. Lizhen Ji, Advanced Lectures in Mathematics, International Press.

P. Guan, Remarks on the homogeneous complex Monge-Amp\`ere equation
Complex Analysis, Trends in Mathematics, Spriner Basel AG. (2010), 175-185.

B. Bian and P. Guan, A structural condition for microscopic convexity principle
Discrete and continuous dynamical systems Volume 28, (2010) 789-807.

P. Guan, Q. Li and X. Zhang, A uniqueness theorem in K\"ahler geometry
Math. Ann. Vol. 345, (2009) 377-393.

B. Bian and P. Guan, A Microscopic Convexity Principle for Nonlinear Partial Differential Equations
Inventiones Mathematicae, V. 177, (2009), 307-335.

P. Guan and J. Li, The quermassintegral inequalities for k-convex starshaped domains,
Advances in Mathematics 221 (2009) 1725-1732.

P. Guan, C.S. Lin and X. Ma, The Existence of Convex Body with Prescribed Curvature Measures
International Mathematics Research Notices, Vol. 2009, (2009) 1947-1975.

P. Guan, X. Ma, N. Trudinger and X. Zhu, A form of Alexandrov-Fenchel inequality
Pure and Applied Mathematics Quarterly, V. 6, (2010), 999-1012.

P. Guan and E. Sawyer, Regularity of Subelliptic Monge-Amp\`{e}re Equations in the Plane
Transactions of American Mathematical Society, Vol. 361, No. 9, (2009), 4581-4591.

B. Bian and P. Guan, Convexity Preserving for Fully Nonlinear Parabolic Integro-Differential Equations
Methods and Applications of Analysis, Vol. 15 (2008), 39-51.

L. Caffarelli, P. Guan and X. Ma, A constant rank theorem for solutions of fully nonlinear elliptic equations
Communications on Pure and Applied Mathematics, V. 60, (2007), 1769-1791

P. Guan and G. Wang, Conformal deformations of the smallest eigenvalue of the Ricci tensor
American Journal of Mathematics, Vol. 129, (2007), 499-526.

P. Guan, C.S. Lin and G. Wang, Local gradient estimates for quotient equations in conformal geometry
International Journal of Mathematics, Vol. 18, No. 4 (2007) 349-361 .

P. Guan, X. Ma and F. Zhou, The Christoffel-Minkowski problem III: existence and convexity of admissible solutions
Communications on Pure and Applied Mathematics, V.59, (2006) 1352-1376.

P. Guan, C.S. Lin and X. Ma, The Christoffel-Minkowski problem II: Weingarten curvature equations
Chinese Annals of Mathematics, Series B. Vol. 27B(6), (2006), 595-614

P. Guan, C.S. Lin and G. Wang, Schouten tensor and some topological properties
Communications in Analysis and Geometry, V.13, No. 5, (2005), pp. 887-902.

P. Guan and G. Wang, Geometric inequalities on locally conformally flat manifolds,
Duke Math. Journal, V.124, (2004), 177-212.

P. Guan, C.S. Lin and G. Wang, Application of The Method of Moving Planes to Conformally Invariant Equations
Mathematische Zeitschrift, V. 247 (2004), pp. 1-19.

P. Guan and X. Ma, Convex solutions of fully nonlinear elliptic equations in classical differential geometry
"Geometric Evolution Equations", Workshop on Geometric Evolution Equations, Edited by S. Chang, B. Chow,
S. Chu and C.S. Lin, Contemp Math. V.367, AMS. (2004)115-128.

Pengfei Guan, Nonlinear Degenerate Elliptic Equations
Proc. of ICCM2001, Taiwan, 2001. Edited by C.S. Lin, L. Yang and S.T. Yau, International Press, (2004), 257-266.

Pengfei Guan and Xinan Ma, The Christoffel-Minkowski problem I: convexity of solutions of a Hessian equation
Inventiones Mathematicae, V.151 (2003), 553-577.

P. Guan and G. Wang, Local estimates for a class of fully nonlinear equations arising from conformal geometry
International Mathematics Research Notices, V. 2003, Issue 26(2003), 1413-1432

Pengfei Guan and Guofang Wang, A fully nonlinear conformal flow on locally conformally flat manifolds
Journal fur die reine und angewandte Mathematik, V. 557 (2003), 219-238.

P. Guan, J. Viaclovsky and G. Wang, Some properties of the Schouten tensor and applications to conformal geometry
Transactions of American Math. Society, V.355 (2003), 925-933.

Bo Guan and Pengfei Guan, Convex Hypersurfaces of Prescribed Curvature
Annals of Mathematics, 156(2002), 655-674.

Pengfei Guan, Extremal Function associated to Intrinsic Norms
Annals of Mathematics, 156(2002), 197-211.

P. Guan, N. Trudinger and X. Wang, On the Dirichlet problem for degenerate Monge-Ampere equations,
Acta Mathematica, V. 182, (1999)pp. 87-104.

Pengfei Guan and Xujia Wang, On a Monge-Ampere Equation Arising in Geometric Optics,
Journal of Differential Geometry, V.48, (1998), 205-222.

Pengfei Guan, $C^2$ A Priori Estimates for Degenerate Monge-Ampere Equations,
Duke Mathematical Journal, V86, (1997), 323-346.

Pengfei Guan and Yanyan Li, $C^{1,1}$ Regularity for Solutions of a Problem of Alexandrov,
Communications on Pure and Applied Mathematics, Vol.50, (1997), 789-811.

Pengfei Guan, Regularity of a Class of Quasilinear Degenerate Ellitpic Equations,
Advances in Mathematics, Vol. 132 (1997), 24-45.

Pengfei Guan and Eric Sawyer, Oblique Derivative Problem,
CRM Proc. and Lecture Notes, Vol.12 (1997), 145-158.

Pengfei Guan, Quasilinear Degenerate Elliptic Equations in Divergence Form,
Contemporary Mathematics, AMS, V205, (1997), 93-100.

Pengfei Guan and Eric Sawyer, Regularity Estimates for Oblique Derivative Problem on Nonsmooth Domains (II),
Chinese Annals of Mathematics, Ser.B., V.17, N.1, (1996),1-36.

Pengfei Guan and Eric Sawyer, Regularity Estiamtes for Oblique Derivative Problem on Nonsmooth Domains (I),
Chinese Annals of Mathematics, Ser.B., V.16, N.3, (1995),299-324.

Pengfei Guan and Yanyan Li, On Weyl Problem With Nonnegative Gauss Curvature.
Journal of Differential Geometry, V.39(1994) 331-342.

Pengfei Guan and Eric Sawyer, Regularity Estimates of Oblique Derivative Problem.
Annals of Mathematics, 137(1993), 1-70.

Pengfei Guan, On An Example of Subelliptic Boundary Value Problem.
Proceedins Symposia in Pure Mathematics,AMS, V.52(1991), 173-177.

Pengfei Guan, Holder Regularity of Subelliptic Pseudo-differential Operators.
Duke Mathematical Journal, V.60(1990), 563-598.