8 papers
Exact counting of spherical metrics with one conical singularity on rectangular tori
Zhijie Chen, Shihong Zhang
We prove that for every integer and , the singular Liouville equation $Δu+\e^u=ρδ_0$ on a rectangular torus $E_{\mathrm{i}b}=\mathbb{C}/(\mathbb Z+\mathrm{…
Conformal Metrics on the unit Ball with Constant -Curvature, Constant -Curvature, and Minimal Boundary
Liming Sun, Heming Wang, Shihong Zhang
We completely classify conformal metrics on the unit ball , , with positive constant -curvature, positive constant -curvature, an…
Sharp weighted Carleman and Huber isoperimetric inequalities on the unit ball in higher dimensions
Zhijie Chen, Changfeng Gui, Shihong Zhang
In this paper, using a limiting approach, we establish a new type of weighted Carleman inequality in all dimensions and classify all extremal functions. In particular, wh…
Sharp quantitative integral inequalities for general conformally invariant extensions
Qiaohua Yang, Shihong Zhang
In this paper, we develop a refined analysis of hypergeometric functions to establish sharp quantitative integral inequalities for a general family of conformally invariant extensi…
A simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball
Runmin Gong, Qiaohua Yang, Shihong Zhang
Frank et al. (J. Funct. Anal., 2022) stated that there is no relation between the reversed Hardy-Littlewood-Sobolev (HLS) inequalities and reverse Sobolev inequalities. However, we…
Classification of solutions to the -flat and constant -curvature equation on the half-space and ball
Xuezhang Chen, Shihong Zhang
For conformal boundary operators associated with the Paneitz operator, we introduce a rigorous definition of the biharmonic Poisson kernel consisting of a pair of kernel functions…
A sharp Sobolev trace inequality of order four on three-balls
Xuezhang Chen, Shihong Zhang
We establish a fourth order sharp Sobolev trace inequality on three-balls, and its equivalence to a third order sharp Sobolev inequality on two-spheres.
Constrained Moser-Trudinger-Onofri inequality and a uniqueness criterion for the mean field equation
Xuezhang Chen, Shihong Zhang
We establish Moser-Trudinger-Onofri inequalities under constraint of a deviation of the second order moments from , which serves as an intermediate one between Chang-Hang's ineq…