A note on the equality case of Bray's conjecture
In this short note, we characterize the equality case of Bray's conjecture recently proved by Jiang-Li-Wang \cite{JLW}.
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arXiv subjects
Xu-Qian Fan
Publications and source records attributed to Xu-Qian Fan.
An existence and uniqueness result for orientation-reversing harmonic diffeomorphism from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$
In this paper, we prove an existence and uniqueness theorem for orientation-reversing harmonic diffeomorphisms from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$ with rotational symmetry, which is a generalization of the corresponding result for dimension $2$.
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A nonexistence result on harmonic diffeomorphisms between punctured spaces
In this paper, we will prove a result of nonexistence on harmonic diffeomorphisms between punctured spaces. In particular, we will given an elementary proof to the nonexistence of rotationally symmetric harmonic diffeomorphisms from the punctured Euclidean space onto the punctured hyperbolic space.
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Steklov eigenvalues on annulus
We obtain supremum of the k-th normalized Steklov eigenvalues of all rotational symmetric conformal metrics on the cylinder with k>1. The case k=1 for all conformal metrics has been completely solved by Fraser and Schoen. We give geometric description in terms of minimal surfaces for metrics attaining the supremum. We also obtain some partial results on the comparison of the normalized Stekov eigenvalues of rotationally symmetric metrics and general conformal metrics on the cylinder. A counter example is constructed to show that for that the first normalized Steklov eigenvalue of rotationally symmetric metric may not be larger.
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Rotationally symmetric harmonic diffeomorphisms between surfaces
In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric on the target.
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A property of the Brown-York mass in Schwarzschild manifolds
We will extend partially our previous results about the limit of the Brown-York mass of a family of convex revolution surfaces in the Schwarzschild manifold such that these surfaces may have unbounded ratios of their radii.
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Product of Almost-Hermitian Manfolds
This is a continuous work about the nonexistence of some complete metrics on the product of two manifolds studied by Tam-Yu [Asian Journal of Mathematics, 14(2010)]. Motivated by the result of Tossati [Comm.Anal.Geom. 15(2007)]. We generalize the corresponding results of Tam-Yu [Asian Journal of Mathematics, 14(2010)] to the almost-Hermitian case.
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The Brown-York mass of revolution surface in asymptotically Schwarzschild manifold
In this paper, we will show that the limit of the Brown-York mass of a family of convex revolution surfaces in an asymptotically Schwarzschild manifold is the ADM mass.
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Large-sphere and small-sphere limits of the Brown-York mass
In this paper, we will study the limiting behavior of the Brown-York mass of the coordinate spheres in an asymptotically flat manifold. Limiting behaviors of volumes of regions related to coordinate spheres are also obtained, including a discussion on the isoperimetric mass introduced by Huisken \cite{Huisken}. We will also study expansions of the Brown-York mass and the Hawking mass of geodesic spheres with center at a fixed point $p$ of a three manifold. Some geometric consequences will be derived.
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