Yong Luo

activity

20112026

most citedHeat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary

51 citations · 163 across the 31 of their papers we have counts for

collaborators

33 papers

math.DG2026

A sharp pinching theorem for closed minimal Legendrian submanifolds

Yong Luo, Linlin Sun, Jiabin Yin

Let $F : M^{n} \to S^{2 n + 1}$ be a minimal Legendrian immersion of a connected closed manifold, where $n \geq 3$ , and let $B$ be its second fundamental form. We prove that if $|B|^2…

math.DG2026

Legendrian submanifolds in the unit sphere with conformal Maslov form and constant sectional curvature

Yong Luo, Cheng Xing

This paper is concerned with the study on Legendrian submanifolds with conformal Maslov form in the unit sphere $S^{2 n + 1}$ , which admits a Sasakian structure $(φ, ξ, η, g)$ f…

math.DG2026

Classification of compact Lagrangian self-similar submanifolds with Legendrian capillary boundary in the unit ball

Dong Gao, Yong Luo, Hui Ma +1

We classify smooth compact connected Lagrangian immersions $X$ in the closed unit ball of $\C^n$, $n \geq 2$ , satisfying $H + ε X^{⊥} = 0$ , $ε \in {- 1, 0, 1}$ , with Le…

math.DG2022

On complete hypersurfaces with constant scalar curvature $n (n - 1)$ in the unit sphere

Jinchuan Bai, Yong Luo

Let $M^{n}$ be an $n$ -dimensional complete and locally conformally flat hypersurface in the unit sphere $S^{n + 1}$ with constant scalar curvature $n (n - 1)$ . We show that if th…

math.AP2021

Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrödinger equations

Yongshuai Gao, Yong Luo

This paper considers ground states of mass subcritical rotational nonlinear Schrödinger equation \begin{equation*} -Δu+V(x)u+iΩ(x^\perp\cdot\nabla u)=μu+ρ^{p-1}|u|^{p-1}u \,\ \text…

math.DG2021

On energy gap phenomena of the Whitney spheres in $C^{n}$ or $CP^{n}$

Yong Luo, Liuyang Zhang

In \cite{Zh} \cite{LY} Zhang, Luo and Yin initiated the study of Lagrangian submanifolds satisfying $\nabla^{*} T = 0$ or $\nabla^{*} \nabla^{*} T = 0$ in $C^{n}$ or $\mathb…

math.AP2021

Concentration Behavior of Ground States for $L^{2}$ -Critical Schrödinger Equation with a Spatially Decaying Nonlinearity

Yong Luo, Shu Zhang

We consider the following time-independent nonlinear $L^{2}$ -critical Schrödinger equation \[ -Δu(x)+V(x)u(x)-a|x|^{-b}|u|^{1+\frac{4-2b}{N}}=μu(x)\,\ \hbox{in}\,\ \mathbb{R}^N, \] w…

math.AP2021

Existence and Asymptotic Behavior of Ground States for Rotating Bose-Einstein Condensates

Yujin Guo, Yong Luo, Shuangjie Peng

We study ground states of two-dimensional Bose-Einstein condensates with repulsive ( $a > 0$ ) or attractive ( $a < 0$ ) interactions in a trap $V (x)$ rotating at the velocity $Ω$ . It is…

math.DG2021

On $n$ -dimensional complete self-similar solutions to the mean curvature flow in $R^{n + 1}$ with nonnegative constant scalar curvature

Yong Luo, Linlin Sun, Jiabin Yin

As is well known, self-similar solutions to the mean curvature flow, including self-shrinkers, translating solitons and self-expanders, arise naturally in the singularity analysis…

math.AP2020★ 17 cited

Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions

Yujin Guo, Yong Luo, Shuangjie Peng

We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap $V (x)$ rotating at the velocity $Ω$ . It is known that there exist a criti…

math.DG2020

Rigidity theorems for minimal Lagrangian surfaces with Legendrian capillary boundary

Yong Luo, Linlin Sun

In this note, we study minimal Lagrangian surfaces in $B^{4}$ with Legendrian capillary boundary on $S^{3}$ . On the one hand, we prove that any minimal Lagrangian sur…

math.DG2020★ 2 cited

On energy gap phenomena of the Whitney sphere and related problems

Yong Luo, Jiabin Yin

In this paper, we study Lagrangian submanifolds satisfying $\nabla^{*} T = 0$ introduced by Zhang \cite{Zh} in the complex space forms $N (4 c) (c = 0 or 1)$ , where $T ={\rm \nabla…

math.DG2019★ 2 cited

A new characterization of the Calabi torus in the unit sphere

Yong Luo, Linlin Sun, Jiabin Yin

In this paper, we study the rigidity theorem of closed minimally immersed Legendrian submanifolds in the unit sphere. Utilizing the maximum principle, we obtain a new characterizat…

math.DG2019

Complete Willmore Legendrian surfaces in $S^{5}$ are minimal Legendrian surfaces

Yong Luo, Linlin Sun

In this paper we continue to consider Willmore Legendrian surfaces and csL Willmroe surfaces in $S^{5}$ , notions introduced by Luo in \cite{Luo}. We will prove that every co…

math.AP2019★ 43 cited

The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with Attractive Interactions

Yujin Guo, Yong Luo, Wen Yang

This article is devoted to studying the model of two-dimensional attractive Bose-Einstein condensates in a trap $V (x)$ rotating at the velocity $Ω$ . This model can be described by…

math.DG2018★ 4 cited

Rigidity of closed CSL submanifolds in the unit sphere

Yong Luo, Linlin Sun

A contact stationary Legendrian submanifold (briefly, CSL submanifold) is a stationary point of the volume functional of Legendrian submanifolds in a Sasakian manifold. Much effort…

math.DG2018

Some remarks on bi-f-harmonic maps and f-biharmonic maps

Yong Luo, Ye-Lin Ou

In this paper, we prove that the class of bi-f-harmonic maps and that of f-biharmonic maps from a conformal manifold of dimension not equal to 2 are the same (Theorem 1.1). We also…

math.DG2018★ 2 cited

A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds

Volker Branding, Yong Luo

In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension $m=\dim M\geq 3$ with infinite volume that admi…

math.FA2018

Limit Behavior of Mass Critical Hartree Minimization Problems with Steep Potential Wells

Yujin Guo, Yong Luo, Zhi-Qiang Wang

We consider minimizers of the following mass critical Hartree minimization problem: \[ e_λ(N):=\underset{\{u\in H^1(R^d),\,\|u\|^2_2=N\}}{\inf} E_λ(u),\,\ d\ge 3, \] where the Hart…

math.DG2018

Nonexistence of proper $p$ -biharmonic maps and Liouville type theorems I: case of $p \geq 2$

Yingbo Han, Yong Luo

Let $u : (M, g) \to (N, h)$ be a map between Riemannian manifolds $(M, g)$ and $(N, h)$ . The $p$ -bienergy of $u$ is defined by $E_{p} (u) = \int_{M} ∣ τ (u) ∣^{p} d ν_{g}$ , where $τ (u)$ is the tensio…

math.DG2017★ 1 cited

Addendum to "Contact stationary Legendrian surfaces in $S^{5}$ "[Pacific Math. J. 293(2018), no.1, 101-120]

Yong Luo

In \cite{Luo}, the present author proved that if $L$ is a contact stationary Legendrian surface in $S^{5}$ with the canonical Sasakian structure and the square length of its…

math.DG2017

Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds

Bingqing Ma, Guangyue Huang, Yong Luo

In this short note, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $Δ u + c u^{α} = 0,$ where $c, α…

math.DG2017

On Willmore Legendrian surfaces in $S^{5}$ and the contact stationary Legendrian Willmore surfaces

Yong Luo

In this paper we study Willmore Legendrian surfaces (that is Legendrian surfaces which are critical points of the Willmore functional). We use an equality proved in \cite{Luo} to g…

math.AP2016★ 51 cited

Heat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary

Tao Huang, Lei Liu, Yong Luo +1

Let $(M, g)$ be a four dimensional compact Riemannian manifold with boundary and $(N, h)$ be a compact Riemannian manifold without boundary. We show the existence of a unique, global…

A sharp pinching theorem for closed minimal Legendrian submanifolds

Legendrian submanifolds in the unit sphere with conformal Maslov form and constant sectional curvature

Classification of compact Lagrangian self-similar submanifolds with Legendrian capillary boundary in the unit ball

On complete hypersurfaces with constant scalar curvature n(n−1) in the unit sphere

Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrödinger equations

On energy gap phenomena of the Whitney spheres in Cn or CPn

Concentration Behavior of Ground States for L2-Critical Schrödinger Equation with a Spatially Decaying Nonlinearity

Existence and Asymptotic Behavior of Ground States for Rotating Bose-Einstein Condensates

On n-dimensional complete self-similar solutions to the mean curvature flow in Rn+1 with nonnegative constant scalar curvature

Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions

Rigidity theorems for minimal Lagrangian surfaces with Legendrian capillary boundary

On energy gap phenomena of the Whitney sphere and related problems

A new characterization of the Calabi torus in the unit sphere

Complete Willmore Legendrian surfaces in S5 are minimal Legendrian surfaces

The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with Attractive Interactions

Rigidity of closed CSL submanifolds in the unit sphere

Some remarks on bi-f-harmonic maps and f-biharmonic maps

A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds

Limit Behavior of Mass Critical Hartree Minimization Problems with Steep Potential Wells

Nonexistence of proper p-biharmonic maps and Liouville type theorems I: case of p≥2

Addendum to "Contact stationary Legendrian surfaces in S5"[Pacific Math. J. 293(2018), no.1, 101-120]

Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds

On Willmore Legendrian surfaces in S5 and the contact stationary Legendrian Willmore surfaces

Heat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary

On complete hypersurfaces with constant scalar curvature $n (n - 1)$ in the unit sphere

On energy gap phenomena of the Whitney spheres in $C^{n}$ or $CP^{n}$

Concentration Behavior of Ground States for $L^{2}$ -Critical Schrödinger Equation with a Spatially Decaying Nonlinearity

On $n$ -dimensional complete self-similar solutions to the mean curvature flow in $R^{n + 1}$ with nonnegative constant scalar curvature

Complete Willmore Legendrian surfaces in $S^{5}$ are minimal Legendrian surfaces

Nonexistence of proper $p$ -biharmonic maps and Liouville type theorems I: case of $p \geq 2$

Addendum to "Contact stationary Legendrian surfaces in $S^{5}$ "[Pacific Math. J. 293(2018), no.1, 101-120]

On Willmore Legendrian surfaces in $S^{5}$ and the contact stationary Legendrian Willmore surfaces