Affine techniques on extremal metrics on toric surfaces
This paper consists of real and complex affine techniques for studying the Abreu equation on toric surfaces. In particular, an interior estimate for Ricci tensor is given.
math.DG↗
arXiv subjects
Li Sheng
Publications and source records attributed to Li Sheng.
Extremal metrics on toric surfaces
In this paper, we study the Abreu equation on toric surfaces. In particular, we prove the existence of the positive extremal metric when relative $K$-stability is assumed.
math.DG↗
Contact Invariants, Open String Invariants and Weinstein Conjecture
We propose a theory of contact invariants and open string invariants, assuming that the almost complex $J$ is either non-degenerate or of Bott-type. We do not choose the complex structure $\tilde{J}$ such that $L_X\tilde{J}=0$ on periodic orbits.
math.SG↗
Exponential decay of $J$-holomorphic maps with finite energy
We prove that every finite energy $J$-holomorphic map $u(s,t):\mathbb R\times S^1 \rightarrow {\mathbb R} \times \widetilde{M}$ exponentially converges to a periodic orbit of Reeb vector field of $\widetilde M,$ as $s\to \infty.$
math.SG↗
Relative Invariants, Contact Geometry and Open String Invariants
In this paper we propose a theory of contact invariants and open string invariants, which are generalizations of the relative invariants. We introduce two moduli spaces $\bar{\mathcal{M}}_{A}(M^{+},C,g,m+ν,{\bf y},{\bf p},(\mathbf{k},\mathfrak{e}))$ and $\bar{\mathcal{M}}_{A}(M,L;g,m+ν,{\bf y},{\bf p},\overrightarrowμ)$, prove the compactness of the moduli spaces and the existence of the invariants.
math.SG↗
Dirac and Weyl Semimetal in XYBi (X=Ba, Eu; Y=Cu, Ag and Au)
Weyl and Dirac semimetals recently stimulate intense research activities due to their novel properties. Combining first-principles calculations and effective model analysis, we predict that nonmagnetic compounds BaYBi (Y=Au, Ag and Cu) are Dirac semimetals. As for the magnetic compound EuYBi, although the time reversal symmetry is broken, their long-range magnetic ordering cannot split the Dirac point into pairs of Weyl points. However, we propose that partially substitute Eu ions by Ba ions will realize the Weyl semimetal.
cond-mat.mtrl-sci↗
Tunable Magnetic Semiconductor Behavior Driven by Half-Filled One Dimensional Band in Zigzag Phosphorene Nanoribbons
An antiferromagnetic insulating state has been found in the zigzag phosphorene nanoribbons (ZPNRs) from a comprehensive density functional theory calculations. Comparing with other one-dimensional systems, the magnetism in ZPNRs display several surprising characteristics: (i) the magnetic moments are antiparallel arranged at each zigzag edge; (ii) the magnetism is quite stable in energy (about 29 meV/magnetic-ion) and the band gap is big (about 0.7 eV); (iii) a moderate compressive strain will induce a magnetic to nonmagnetic as well as semiconductor to metal transition. All of these phenomena arise naturally due to one unique mechanism, namely the electronic instability induced by the half-filled one dimensional bands which cross the Fermi level at around π/2a. The unusual electronic and magnetic properties in ZPNRs endow them great potential for the applications in nanoelectronic devices.
cond-mat.mes-hall↗
On Uniqueness of Complete Ricci Flow Solution with Curvature Bounded from Below
Let $(M,g)$ be a complete noncompact non-collapsing $n$-dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded from above. Then ricci flow with above as its initial data, has at most one solution in the class of complete riemannian metric with complex sectional curvature bounded from below.
math.DG↗
Interior Estimates for the $n$-dimensional Abreu's Equation
We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.
math.DG↗
Microscopic Mechanism of Stereochemically Active Lone Pair Studied from Orbital Selective External Potential Calculation
The nature of the stereochemically active lone pair has long been in debate. Here, by application of our recently developed orbital selective external potential (OSEP) method, we have studied the microscopic mechanism of stereochemically active lone pairs in various compounds. The OSEP method allows us to shift the energy level of specific atomic orbital, therefore is helpful to identify unambiguously the role of this orbital to the chemical and physical properties of the system we are interested in. Our numerical results, with compelling proofs, demonstrate that the on-site mixing of cation valence s orbital with the nominally empty p orbitals of the same subshell is crucial to the formation of lone pair, whereas the anion p orbital has only small effect. Our detailed investigation of Sn and Pb monochalcogenides show that structures of these systems have significant effects on lone pairs. In return, the formation of lone pair, which can be controlled by our OSEP method, could result in structural instabilities of Sn and Pb monochalcogenides.
cond-mat.mtrl-sci↗
The interior regularity of the Calabi flow on a toric surface
Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t < T.
math.DG↗
Electronic structure and magnetic properties of NaOsO$_{3}$
A comprehensive investigation of the electronic and magnetic properties of NaOsO3 has been made using the first principle calculations, in order to understand the importance of Coulomb interaction, spin-orbit coupling and magnetic order in its temperature-induced and magnetic-related metal-insulator transition. It is found that its electronic structure near the Fermi energy is dominated by strongly hybridized Os 5d and O 2p states. Despite of the large strength of spin-orbit coupling, it has only small effect on the electronic and magnetic properties of NaOsO3. On the other hand, the on-site Coulomb repulsion affects the band structure significantly, but, a reasonable U alone cannot open a band gap. Its magnetism is itinerant, and the magnetic configuration plays an important role in determining the electronic structure. Its ground state is of a G-type antiferromagnet, and it is the combined effect of U and magnetic configuration that results in the insulating behavior of NaOsO3.
cond-mat.str-el↗
Uniform K-stability for extremal metrics on toric varieties
In this paper we prove that for toric varieties the uniform K-stability is the necessary condition for the existence of extremal metrics.
math.DG↗
Interior regularity on the Abreu equation
In this paper we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the $C^0$ estimate.
math.DG↗
The Kahler Metrics of constant scalar curvature on the Complex Torus
We study the Dirichlet problem of the Abreu equation. The solutions provide the Kahler metrics of constant scalar curvature on the complex torus.
math.DG↗
Quantum Phase Transition in Hall Conductivity on an Anisotropic Kagome Lattice
We study the quantum Hall effect(QHE) on the Kagomé lattice with anisotropy in one of the hopping integrals. We find a new type of QHE characterized by the quantization rules for Hall conductivity $σ_{xy}=2ne^{2}/h$ and Landau Levels $E(n)=\pm v_{F}\sqrt{(n+1/2)\hbar Be}$ ($n$ is an integer), which is different from any known type. This phase evolves from the QHE phase with $σ_{xy}=4(n+1/2)e^{2}/h$ and $E(n)=\pm v_{F}\sqrt{2n\hbar Be}$ in the isotropic case, which is realized in a system with massless Dirac fermions (such as in graphene). The phase transition does not occur simultaneously in all Hall plateaus as usual but in sequence from low to high energies, with the increase of hopping anisotropy.
cond-mat.mes-hall↗
Probabilistic Analysis of Rule 2
Li and Wu proposed Rule 2, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. Here we study the asymptotic performance of Rule 2 on random unit disk graphs formed from n random points in an s_n by s_n square region of the plane. If s_n is below the threshold for connectivity, then Rule 2 produces a dominating set whose expected size is O(n/(loglog n)^{3/2}). We conjecture that this bound is not optimal.
cs.DM↗