2 citations · 14 across the 13 of their papers we have counts for
14 papers
On potentials for sub-Laplacians and geometric applications
Shiguang Ma, Jie Qing
In this paper we extend the research on potential theory and its geometric applications from Euclidean spaces to homogeneous Carnot groups. We introduce a new approach to use the g…
Potential theory and applications in conformal geometry
Shiguang Ma, Jie Qing
In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to st…
On the asymptotic behavior of p-superharmonic functions at singularities
Huajie Liu, Shiguang Ma, Jie Qing +1
In this paper we develop the p-thinness and the p-fine topology for the asymptotic behavior of p-superharmonic functions at singular points. We consider these as extensions of earl…
p-Laplace equations in conformal geometry
Huajie Liu, Shiguang Ma, Jie Qing +1
In this paper we introduce the p-Laplace equations for the intermediate Schouten curvature in conformal geometry. These p-Laplace equations provide more tools for the study of geom…
Linear potentials and applications in conformal geometry
Shiguang Ma, Jie Qing
In this paper we derive estimates for linear potentials that hold away from thin subsets. And, inspired by the celebrated work of Huber, we verify that, for a subset that is thin a…
On Huber's type theorems in general dimensions
Shiguang Ma, Jie Qing
In this paper we present some extensions of the celebrated finite point conformal compactification theorem of Huber \cite{Hu57} for complete open surfaces to general dimensions bas…
On -superharmonic functions and some geometric applications
Shiguang Ma, Jie Qing
In this paper we study asymptotic behavior of -superharmonic functions at isolated singularity using the Wolff potential and -capacity estimates in nonlinear potential theory…
Rigidity of the hexagonal Delaunay triangulated plane
Song Dai, Huabin Ge, Shiguang Ma
We show the rigidity of the hexagonal Delaunay triangulated plane under Luo's PL conformality. As a consequence, we obtain a rigidity theorem for a particular type of locally finit…
Hypersurfaces with nonnegative Ricci curvature in hyperbolic space
Vincent Bonini, Shiguang Ma, Jie Qing
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymp…
On nonnegatively curved hypersurfaces in hyperbolic space
Vincent Bonini, Shiguang Ma, Jie Qing
In this paper we prove the conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved…
Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds
Shiguang Ma
In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlyin…
Constant mean curvature surfaces of Delaunay type along a closed geodesic
Shiguang Ma
In this paper, we construct Delaunay type constant mean curvature surfaces along a nondegenerate closed geodesic in a 3-dimensional Riemannian manifold.
On the radius pinching estimate and uniqueness of the CMC foliation in asymptotically flat 3-manifolds
Shiguang Ma
In this paper we consider the uniqueness problem of the constant mean curvature spheres in asymptotically flat 3-manifolds. We require the metric have the form g_{ij}=δ_{ij}+h_{ij}…
Uniqueness of the Foliation of Constant Mean Curvature Spheres in Asymptotically Flat 3-Manifolds
Shiguang Ma
In this paper I study the constant mean curvature surface in asymptotically flat 3-manifolds with general asymptotics. Under some weak condition, I prove that outside some compact…