On the behavior of quasi-local mass at the infinity along nearly round surfaces (2008)
Shi, Yuguang, Wang, Guofang, Wu, Jie
In this paper, we study the limiting behavior of the Brown-York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined...
Metrics of constant curvature on a Riemann surface with two corners on the boundary (2007)
Jost, Juergen, Wang, Guofang, Zhou, Chunqin
We use PDE methods as developed for the Liouville equation to study the existence of conformal metrics with prescribed singularities on surfaces with boundary, the boundary condition being constant...
Liouville Theorems for Dirac-Harmonic Maps (2007)
Chen, Qun, Jost, Juergen, Wang, Guofang
We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space $\R^n$, the hyperbolic space $\H^n$ and a Riemannian manifold $\mathfrak{S^n}$ ($n\geq 3$) with the Schwarzschild metric...
Jurgen Jost, J Urgen, Guofang Wang, Guofang Wang
Classification of solutions of a toda system in R 2 by
Abstract. In ths paper, we consider the following problem (PM): \Deltau + jxj fi
Nonlinear Dirac equations on Riemann surfaces (2007)
Chen, Qun, Jost, Juergen, Wang, Guofang
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass...
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
On a Conformal Quotient Equation (2007)
In this paper, we continue our work [7] to consider a conformal quotient equation $$\frac{{\sigma }_{2}(g)}{{\sigma }_{1}(g)}=1$$ in a given conformal class and prove the existence for n > 4.
Transverse K\"ahler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds (2006)
Futaki, Akito, Ono, Hajime, Wang, Guofang
In this paper we study compact Sasaki manifolds in view of transverse K\"ahler geometry and extend some results in K\"ahler geometry to Sasaki manifolds. In particular we define integral invariants...
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...
Super-Liouville Equations on Closed Riemann Surfaces (2005)
Jost, Juergen, Wang, Guofang, Zhou, Chunqin
Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is...
On a fully nonlinear Yamabe problem (2005)
We solve the $\sigma_2$-Yamabe problem for a non locally conformally flat manifold of dimension $n>8$.
Analytic Aspects of the Toda System: II. Bubbling behavior and existence of solutions (2005)
Jost, Jürgen, Lin, Chang-Shou, Wang, Guofang
In this paper, we continue to consider the 2-dimensional (open) Toda system (Toda lattice) for $SU(N+1)$. We give a much more precise bubbling behavior of solutions and study its existence in some...
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...
Chen, Qun, Jost, Juergen, Li, Jiayu, Wang, Guofang
We introduce a functional that couples the nonlinear sigma model with a spinor field: $L=\int_M[|d\phi|^2+(\psi,\D\psi)]$. In two dimensions, it is conformally invariant. The critical points of this...
Regularity Theorems and Energy Identities for Dirac-Harmonic Maps (2004)
Chen, Qun, Jost, Juergen, Wang, Guofang, Li, Jiayu
We study a new set of coupled field equations motivated by the non-linear supersymmetric sigma model of quantum field theory. These equations couple a map into a Riemannian manifold controlled by a...
Mean curvature flow with flat normal bundles (2004)
Smoczyk, Knut, Wang, Guofang, Xin, Y. L.
We show that flatness of the normal bundle is preserved under the mean curvature flow in the Euclidean space and use this to generalize a classical result for hypersurfaces due to Ecker-Huisken in...
Mean curvature flow with flat normal bundles (2004)
Smoczyk, Knut, Wang, Guofang, Xin, Yuanlong
We show that flatness of the normal bundle is preserved under the mean curvature flow in and use this to generalize a classical result for hypersurfaces by Ecker & Huisken in the case of submanifolds...
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...
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.
Classification of solutions of a Toda system in R2 (2002)
We consider solutions of the following (open) Toda system (Toda lattice) for SU(N + 1)$$-\frac{1}{2}\Delta {u}_{i}=\sum _{j=1}^{N}{a}_{ij}\hbox{ \hspace{0.17em} }{e}^{{u}_{j}}\hbox{ \hspace{0.17em}...
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...
Classification of solutions of a Toda system in R^2 (2001)
We consider solutions of a Toda system for SU(N+1) and show that any solution with finite exponential integral cam be obtained from a rational curve in complex projective space of dimension N
Analytic aspects of the Toda system: I. A Moser-Trudinger inequality (2000)
We analyze solutions of the Toda system and establish an optimal Moser-Trudinger inequality
Equivariant and Bott-type Seiberg-Witten Floer Homology: Part I (1999)
We construct Bott-type and equivariant Seiberg-Witten Floer homology and cohomology for 3-manifolds, in particular rational homology spheres, and prove their diffeomorphism invariance. This paper is...
On a Conjecture of Wolansky (1999)
Guofang Wang, Guofang Wang, Jun-Cheng Wei, Jun-cheng Wei
. In ths paper, we consider the following problem (PM ) : \Deltau + jxj fi e u = 0; x 2 BR ; \Gamma Z @BR @u @ = M; u = 0 on @BR ; where is an unknown constant, fi ? 0, BR = fx 2 R 2 jjxj ! Rg, M is...
Jürgen Jost, Weiyue Ding, Weiyue Ding, J Urgen Jost, Jiayu Li, Jiayu Li, ...
. The abelian Chern-Simons-Higgs model of Hong-Kim-Pac and JackiwWeinberg leads to a Ginzburg-Landau type functional with a 6 th order potential on a compact Riemann surface. We derive the existence...
Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere (1998)
Weiyue Ding, Weiyue Ding, Jürgen Jost, Jurgen Jost, Jiayu Li, Jiayu Li, ...
We consider a Ginzburg-Landau type functional on S 2 with a 6 th order potential and the corresponding selfduality equations. We study the limiting behavior in the two vortex case when a coupling...
Existence Results for Mean Field Equations (1997)
Jürgen Jost, Weiyue Ding, Weiyue Ding, J Urgen Jost, Jiayu Li, Jiayu Li, ...
. Let\Omega be an annulus. We prove that the mean field equation \Gamma\Delta/ = e \Gammafi/ R\Omega e \Gammafi/ in\Omega / = 0 on @\Omega admits a solution for fi 2 (\Gamma16ß; \Gamma8ß). This is...
Variational Aspects of the Seiberg-Witten Functional (1995)
Jost, Juergen, Peng, Xiaowei, Wang, Guofang
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line...