Description of surfaces associated with $CP^{N-1}$ sigma models on Minkowski space

Lorentz-Minkowski 3-空间中的模曲面：曲率与应用

Modular Surfaces in Lorentz-Minkowski 3-Space: Curvature and Applications

本文研究 Lorentz-Minkowski 3-空间中模曲面曲率符号与复解析函数零点的关系，完全分类零高斯曲率模曲面，证明非平面极大模曲面不存在，并展示其在共形场论与非线性 sigma 模型中的应用。

Timelike surfaces into 4-dimensional Minkowski space via spinors

We prove that an isometric immersion of a timelike surface in four-dimensional Minkowski space is equivalent to a normalized spinor field which is a solution of a Dirac equation on the surface. Using the quaternions and the complex numbers, we obtain a spinor representation formula that relates the spinor field and the isometric immersion. Applying the representation formula, we deduce a new spinor representation of a timelike surface in three-dimensional De Sitter space; we give a formula for the Laplacian of the Gauss map of a minimal timelike surface in four-dimensional Minkowski space in t…

超临界对偶 k-Minkowski 流与一般给定数据：先验估计与渐近收敛

Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence

本文研究超临界对偶 k-Minkowski 流的长时间行为，证明其从任意严格凸初始曲面指数收敛到唯一严格凸稳态解，并给出显式收敛速率与唯一性。

Evolutes of plane curves and null curves in Minkowski $3$-space

We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski $3$-space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the corresponding plane curves. This leads to an alternative description of all plane curves which are Laguerre congruent to a given one.

Heinz型平均曲率估计在Lorentz-Minkowski空间中的研究

Heinz-type mean curvature estimates in Lorentz-Minkowski space

本文在Lorentz-Minkowski空间中，在梯度有界条件下统一了Heinz型平均曲率估计，并推导出常平均曲率整图的消失定理。

Completeness of convex entire surfaces in Minkowski 3-space

We prove four results towards a description, in terms of the null support function, of the set of isometric embeddings of the hyperbolic plane into Minkowski 3-space. We show that for sufficiently tame null support function, the corresponding entire surface of constant curvature -1 is complete, and for sufficiently sharp null support function, it is incomplete. Our results apply also to entire surfaces whose curvature is merely bounded.

Riemann Zero Mean Curvature Examples in Lorentz-Minkowski Space

Riemann zero mean curvature examples in the Lorentz-Minkowski space are surfaces with zero mean curvature foliated by circles contained in parallel planes. In contrast to the Euclidean case, this family of surfaces presents new and rich features because of the variety of types of circles. In this paper, we give a geometric description of these examples when the circles are contained in spacelike planes and timelike planes.

Reconstructing Minkowski Space-Time

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of the light-cone. We focus on the gravitational aspects of the duality. Specifically, we identify the gravitational holographic data and provide the way Minkowski space-time (understood in more general context as a Ricci-flat space) is reconstructed from the data. In order to avoid…

A class of anisotropic expanding curvature flows

We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_k is the k-th symmetric polynomial of the principle curvature radii of the hypersurface, k is an integer and 1<= k<= n. We prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalisation, to a soliton which is a solution of a elliptic equation, when the constants alpha, beta bel…

Lorentz-Minkowski 空间中的极大平移曲面

Maximal translation surfaces in Lorentz-Minkowski space

本文分类了 Lorentz-Minkowski 空间中由两条空间曲线之和生成的极大平移曲面，证明了生成曲线的平面性相互蕴含，并推广了 Scherk 曲面，同时构造了欧氏空间中不存在对应物的伪零曲线型新例子。

Surfaces associated with sigma models and the sine-Gordon equation

We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional surfaces immersed in the su(N) algebra. In the special case of the CP^1 sigma model we obtain constant negative Gaussian curvature surfaces. As a consequence, this leads us to an explicit relation between the CP^1 sigma model and the sine-Gordon equation.

Spacelike surfaces in Minkowski space satisfying a linear relation between their principal curvatures

In this work, we consider spacelike surfaces in Minkowski space $\hbox{\bf E}%_{1}^{3}$ that satisfy a linear Weingarten condition of type $κ_{1}=mκ_{2}+n$, where $m$ and $n$ are constant and $κ_{1}$ and $κ_{2}$ denote the principal curvatures at each point of the surface. We study the family of surfaces foliated by a uniparametric family of circles in parallel planes. We prove that the surface must be rotational or the surface is part of the family of Riemann examples of maximal surfaces ($m=-1$, $n=0$). Finally, we consider the class of rotational surfaces for the case $n=0$, obtaining a fir…

Geometry of D-branes for general N=(2,2) sigma models

We give a world-sheet description of D-brane in terms of gluing conditions on T+T^*. Using the notion of generalized Kahler geometry we show that A- and B-types D-branes for the general N=(2,2) supersymmetric sigma model (including a non-trivial NS-flux) correspond to the (twisted) generalized complex submanifolds with respect to the different (twisted) generalized complex structures however.