51 citations · 66 across the 17 of their papers we have counts for
17 papers
The blow-up analysis of an affine Toda system corresponding to superconformal minimal surfaces in
Lei Liu, Guofang Wang
In this paper, we study the blow-up analysis of an affine Toda system corresponding to minimal surfaces into [19]. This system is an integrable system which is a na…
Harmonic maps with free boundary from degenerating bordered Riemann surfaces
Lei Liu, Chong Song, Miaomiao Zhu
We study the blow-up analysis and qualitative behavior for a sequence of harmonic maps with free boundary from degenerating bordered Riemann surfaces with uniformly bounded energy.…
On the -th Eigenvalue of Sturm-Liouville Problem and the Maslov Index
Xijun Hu, Lei Liu, Li Wu +1
In the previous papers \cite{HLWZ,KWZ}, the jump phenomena of the -th eigenvalue were completely characterized for Sturm-Liouville problems. In this paper, we show that the jump…
The number of languages with maximum state complexity
Bjørn Kjos-Hanssen, Lei Liu
Câmpeanu and Ho (2004) determined the maximum finite state complexity of finite languages, building on work of Champarnaud and Pin (1989). They stated that it is very difficult to…
Global existence of the harmonic map heat flow into Lorentzian manifolds
Xiaoli Han, Juergen Jost, Lei Liu +1
We investigate a parabolic-elliptic system for maps from a compact Riemann surface into a Lorentzian manifold with a warped product metric. That s…
The qualitative behavior at the free boundary for approximate harmonic maps from surfaces
Juergen Jost, Lei Liu, Miaomiao Zhu
Let be a sequence of maps from a compact Riemann surface with smooth boundary to a general compact Riemannian manifold with free boundary on a smooth submanifold…
Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary
Juergen Jost, Lei Liu, Miaomiao Zhu
For a sequence of coupled fields from a compact Riemann surface with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and…
A global weak solution to the Lorentzian harmonic map flow
Xiaoli Han, Lei Liu, Liang Zhao
We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product…
Singularity of the -th eigenvalue of high dimensional Sturm-Liouville problems
Xijun Hu, Lei Liu, Li Wu +1
It is natural to consider continuous dependence of the -th eigenvalue on -dimensional () Sturm-Liouville problems after the results on -dimensional case by Kong, W…
Multiplicity of closed characteristics on -symmetric compact convex hypersurfaces in
Lei Liu, Li Wu
There is a long standing conjecture that there are at least closed characteristics for any compact convex hypersurface in , and the symmetric case, i.e. $Σ…
Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold
Jiayu Li, Lei Liu
In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map…
Heat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary
Tao Huang, Lei Liu, Yong Luo +1
Let be a four dimensional compact Riemannian manifold with boundary and be a compact Riemannian manifold without boundary. We show the existence of a unique, global…
Blowup behavior of harmonic maps with finite index
Yuxiang Li, Lei Liu, Youde Wang
In this paper, we study the blow-up phenomena on the -harmonic map sequences with bounded uniformly -energy, denoted by $\{u_{α_k}: α_k>1 \quad \mbox{and} \quad α_k\searr…
Topological pressure dimension for almost additive potentials
Lei Liu, Huajun Gong, Xiaoyao Zhou
This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate funda…
Preimage entropy dimension of topological dynamical systems
Lei Liu, Xiaomin Zhou, Xiaoyao Zhou
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and co…
On the finite time blow-up of biharmonic map flow in dimension four
Lei Liu, Hao Yin
In this paper, we show that for certain initial values, the (extrinsic) biharmonic map flow in dimension four must blow up in finite time.
Neck analysis for biharmonic maps
Lei Liu, Hao Yin
In this paper, we study the blow up of a sequence of (both extrinsic and intrinsic) biharmonic maps in dimension four with bounded energy and show that there is no neck in this pro…