Xiaobao Zhu

activity

20122023

most citedA singular Moser-Trudinger inequality for mean value zero functions in dimension two

5 citations · 11 across the 14 of their papers we have counts for

collaborators

14 papers

math.DG2023

Liouville Theorem for Harmonic Maps from Riemannian Manifold with Compact Boundary

Jun Sun, Xiaobao Zhu

In this note we will provide a gradient estimate for harmonic maps from a complete noncompact Riemannian manifold with compact boundary (which we call "Kasue manifold") into a simp…

math.AP2023

A singular Kazdan-Warner problem on a compact Riemann surface

Xiaobao Zhu

Let $(M, g)$ be a compact Riemann surface with unit area, $h \in C^{\infty} (M)$ a function which is positive somewhere, $ρ > 0$ , $p_{i} \in M$ and $α_{i} \in (- 1, + \infty)$ for $i=1,\cdots,\el…

math.DG2022

Another remark on a result of Ding-Jost-Li-Wang

Xiaobao Zhu

Let $(M, g)$ be a compact Riemann surface, $h$ be a positive smooth function on $M$ . It is well known the functional $$J(u)=\frac{1}{2}\int_M|\nabla u|^2dv_g+8π\int_M udv_g-8π\log\i…

math.AP2020★ 5 cited

A singular Moser-Trudinger inequality for mean value zero functions in dimension two

Xiaobao Zhu

Let $Ω \subset R^{2}$ be a smooth bounded domain with $0 \in \partial Ω$ . In this paper, we prove that for any $β \in (0, 1)$ , the supremum $$\sup_{u\in W^{1,2}(Ω), \int_Ωu dx=0, \i…

math.AP2018★ 1 cited

Mean field equations on a closed Riemannian surface with the action of an isometric group

Yunyan Yang, Xiaobao Zhu

Let $(Σ, g)$ be a closed Riemannian surface, $G = {σ_{1}, \dots, σ_{N}}$ be an isometric group acting on it. Denote a positive integer $ℓ = in f_{x \in Σ} I (x)$ , where $I (x)$ is t…

math.AP2018★ 1 cited

A Trudinger-Moser inequality for conical metric in the unit ball

Yunyan Yang, Xiaobao Zhu

In this note, we prove a Trudinger-Moser inequality for conical metric in the unit ball. Precisely, let $B$ be the unit ball in $R^{N}$ $(N \geq 2)$ , $p > 1$ , $g=|x|^{…

math.AP2017

Prescribing Gaussian curvature on closed Riemann surface with conical singularity in the negative case

Yunyan Yang, Xiaobao Zhu

The problem of prescribing Gaussian curvature on Riemann surface with conical singularity is considered. Let $(Σ, β)$ be a closed Riemann surface with a divisor $β$ , and $K_{λ} = K + λ$ ,…

math.AP2017

Existence of solutions to a class of Kazdan-Warner equations on compact Riemannian surface

Yunyan Yang, Xiaobao Zhu

Let $(Σ, g)$ be a compact Riemannian surface without boundary and $λ_{1} (Σ)$ be the first eigenvalue of the Laplace-Beltrami operator $Δ_{g}$ . Let $h$ be a positive smooth function on $…

math.DG2016

A generalized Trudinger-Moser inequality on a compact Riemannian surface

Xiaobao Zhu

Let $(Σ, g)$ be a compact Riemannian surface. Let $ψ$ , $h$ be two smooth functions on $Σ$ with $\int_{Σ} ψ d v_{g} \neq = 0$ and $h \geq 0$ , $h \neq \equiv 0$ . In this paper, using a method of b…

math.AP2016★ 1 cited

Blow-up analysis concerning singular Trudinger-Moser inequalities in dimension two

Yunyan Yang, Xiaobao Zhu

In this paper, we derive a sharp version of the singular Trudinger-Moser inequality, which was originally established by Adimurthi and Sandeep (Nonlinear Differ. Equ. Appl. 2007).…

math.AP2016★ 1 cited

A remark on a result of Ding-Jost-Li-Wang

Yunyan Yang, Xiaobao Zhu

Let $(M, g)$ be a compact Riemannian surface without boundary, $W^{1, 2} (M)$ be the usual Sobolev space, $J : W^{1, 2} (M) \to R$ be the functional defined by $$J(u)=\fr…

math.AP2015

An improved Hardy-Trudinger-Moser inequality

Yunyan Yang, Xiaobao Zhu

Let $B$ be the unit disc in $R^{2}$ , $H$ be the completion of $C_{0}^{\infty} (B)$ under the norm $$\|u\|_{\mathscr{H}}=\left(\int_\mathbb{B}|\nabla u…

math.DG2013

Trudinger-Moser embedding on the hyperbolic space

Yunyan Yang, Xiaobao Zhu

In [16], we established Trudinger-Moser inequalities for complete noncompact Riemannian manifold on which the Ricci curvature has lower bound and the injectivity radius is strictly…

math.AP2012★ 2 cited

A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space

Yunyan Yang, Xiaobao Zhu

In this note, we give a new proof of subcritical Trudinger-Moser inequality on $R^{n}$ . All the existing proofs on this inequality are based on the rearrangement argument wi…