相关论文: Equations of Parametric Surfaces with Base Points …

For a $d$-dimensional hypersurface of class $C^3$ without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplacians. We then use this elliptic reformulation as a basis for…

The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…

Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We…

We construct examples of smooth surfaces S in P^6 with no trisecant lines. This list includes examples of surfaces not cut out by quadrics. We prove that unless S has a finite number of disjoint $(-1)$-lines, and each one meets some other…

In this article we prove some strong vanishing theorems on K3 surfaces. As an aplication of them, we obtain higher syzygy results for K3 surfaces and Fano varieties.

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study…

In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic geometric partial differential equations. Examples…

The goal of this note is to quantitatively study the behavior of asymptotic syzygies for certain toric surfaces, including Hirzebruch surfaces. In particular, we show that the asymptotic linear syzygies of Hirzebruch surfaces embedded by…

Let Y be a surface with only finitely many singularities all of which are cusps. A set of cusps on Y is called three-divisible, if there is a cyclic global triple cover of Y branched precisely over these cusps. The aim of this note is to…

Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…

The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation…

This treats the base-point-freeness of the adjoint bundles on normal surfaces with a boundary. This is an extension of the non-relative version of the theorem of Ein-Lazarsfeld-Masek and the theorem of Kawachi-Masek.

Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…

We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…

Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…

A fundamental theorem of Laman characterises when a bar-joint framework realised generically in the Euclidean plane admits a non-trivial continuous deformation of its vertices. This has recently been extended in two ways. Firstly to…

In this research article, we discuss two topics. Firstly, we introduce SCC-Map and $\phi$-contraction type $T$-coupling. By using these two definitions, we generalize $\phi$-contraction type coupling given by H. Aydi et al. [3] to…

We derive the Pauli equation for a charged spin particle confined to move on a spatially curved surface $\mathcal{S}$ in an electromagnetic field. Using the thin-layer quantization scheme to constrain the particle on $\mathcal{S}$, and in…

Let $X$ be the projective plane, a Hirzebruch surface, or a general $K3$ surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on $X$. We…

A graph $G=(V,E)$ is a support of a hypergraph $H=(V,S)$ if every hyperedge induces a connected subgraph in $G$. Supports are used for certain types of hypergraph visualizations. In this paper we consider visualizing spatial hypergraphs,…