Related papers: Circle packings on surfaces with projective struct…

Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian pairing on this space with values in the complex vector space…

We present an approach of computing the intersection curve $\mathcal{C}$ of two rational parametric surface $\S_1(u,s)$ and $\S_2(v,t)$, one being projectable and hence can easily be implicitized. Plugging the parametric surface to the…

Let $S$ be a closed orientable surface of genus at least two. We introduce a bordification of the moduli space $\mathcal{PT}(S)$ of complex projective structures, with a boundary consisting of projective classes of half-translation…

This paper presents an efficient approach for the conceptual design of architectural surfaces which are composed of triangular panels. In the free-form design of discrete architectural surfaces, the Gaussian curvature plays an important…

Let $\mathbf{\Sigma}=(\Sigma,M,O)$ be a surface with marked points and order-2 orbifold points which is either unpunctured or once-punctured closed, and $\omega:O\rightarrow\{1,4\}$ a function. For each triangulation $\tau$ of…

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\pi_1(\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$…

We show that the hyperkahler geometry of $T^*\mathbb{CP}^{n-1}$ can be described algebraically by the affine scheme of rank-1 projections, and that this description simultaneously yields explicit $SU(n)$-equivariant isometric embeddings \[…

Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…

A natural and intrinsic characterization of the structure of the set $\mathfrak{C}$ of positive unital maps is given, i.e. it is shown that $\mathfrak{C}$ is isometrically isomorphic to the subset $\gD$ of bp-positive density matrices…

Let $\rho_\Sigma=h(|z|^2)$ be a metric in a Riemann surface $\Sigma$, where $h$ is a positive real function. Let $\mathcal H_{r_1}=\{w=f(z)\}$ be the family of univalent $\rho_\Sigma$ harmonic mapping of the Euclidean annulus…

Call a periodic map $h$ on the closed orientable surface $\Sigma_g$ extendable if $h$ extends to a periodic map over the pair $(S^3, \Sigma_g)$ for possible embeddings $e: \Sigma_g\to S^3$. We determine the extendabilities for all…

We study analytic descriptions of conformal immersions of the Riemann sphere S^2 into the CP^(N-1) sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is…

Circle packing is widely used in visualization due to its aesthetic appeal and simplicity, particularly in tasks where the spatial arrangement and relationships between data are of interest, such as understanding proximity relationships…

We prove that the mirror map is the SYZ map for every toric Calabi-Yau surface. As a consequence one obtains an enumerative meaning of the mirror map. This involves computing genus-zero open Gromov-Witten invariants, which is done by…

We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason - the problem of "super…

The immersion of the string world sheet, regarded as a Riemann surface, in $R^3$ and $R^4$ is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain…

We study the gluing theory of Riemann surfaces using formal algebraic geometry, and give computable relations between the associated parameters for different gluing processes. As its application to the Liouville conformal field theory, we…

We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably…

Circle packings with specified patterns of tangencies form a discrete counterpart of analytic functions. In this paper we study univalent packings (with a combinatorial closed disk as tangent graph) which are embedded in (or fill) a…

Via the transverse Hilbert scheme construction, we associate a holomorphic completely integrable system to a surface $S$ endowed with a holomorphic symplectic form $\omega$ and a projection onto $\mathbb{C}$. We provide a full…