Regularity of the geodesic equation in the space of Sasakian metrics (2009)
This paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics. Firstly, we reduce the geodesic equation in the space of Sasakian metrics to a Dirichlet...
A Microscopic Convexity Principle for Nonlinear Partial Differential Equations (2008)
We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.
The quermassintegral inequalities for starshaped domains (2007)
We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt \cite{G} and Urbas \cite{U} on an expanding geometric...
Conformal deformations of the smallest eigenvalue of the Ricci tensor (2007)
Guan, Pengfei., Wang, Guofang.
American Journal of Mathematics - Volume 129, Number 2, April 2007
Schouten tensor and some topological properties (2005)
Guan, Pengfei, Lin, Chang-Shou, Wang, Guofang
In this paper, we prove a cohomology vanishing theorem on locally conformally flat manifold under certain positivity assumption on the Schouten tensor. And we show that this type of positivity of...
Conformal deformations of the smallest eigenvalue of the Ricci tensor (2005)
We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor to be a constant. It is related to the notion of minimal volumes in comparison...
Extremal function of intrinsic norms (2004)
Through the study of the degenerate complex Monge-Amp\`ere equation, we establish the optimal regularity of the extremal function associated to intrinsic norms of Chern-Levine-Nirenberg and...
Geometric inequalities on locally conformally flat manifolds (2004)
Through the study of some elliptic and parabolic fully nonlinear partial differential equations, we establish conformal versions of the quermass-integral inequality, the Sobolev inequality, and the...
Geometric inequalities on locally conformally flat manifolds (2003)
Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for...
Local estimates for a class of fully nonlinear equations arising from conformal geometry (2003)
Pengfei Guan, Pengfei Guan, Guofang Wang, Guofang Wang
Local estimates for a class of fully nonlinear equations arising from conformal geometry by
Local estimates for a class of fully nonlinear equations arising from conformal geometry (2003)
We establish local gradient estimates for fully nonlinear partial differential equations involving elementary symmetric functions of Schouten tensor in conformal geometry. We also obtain local second...
The extremal function associated to intrinsic norms (2002)
Through the study of the degenerate complex Monge-Ampère equation, we establish the optimal regularity of the extremal function associated to intrinsic norms of Chern-Levine-Nirenberg and...
Some properties of the Schouten tensor and applications to conformal geometry (2002)
Guan, Pengfei, Viaclovsky, Jeff, Wang, Guofang
The note is about some nonlinear curvature conditions which arise naturally in conformal geometry.
A fully nonlinear conformal flow on locally conformally flat manifolds (2001)
We study a fully nonlinear flow for conformal metrics. The long-time existence and the sequential convergence of flow are established for locally conformally flat manifolds. As an application, we...
A form of Alexandrov-Fenchel inequality (2001)
Pengfei Guan, Pengfei Guan, Xi-nan Ma, Xi-nan Ma, Neil Trudinger, Neil Trudinger, ...
by
estimates for solutions of a problem of Alexandrov (1996)
this paper that when the density of ¯ is smooth and nonnegative, solutions to the Alexandrov problem are at least C
H"older regularity of subelliptic pseudo-differential operators /--Pengfei Guan. (1989)
Thesis (Ph. D.)--Princeton University, 1989.