Related papers: Efficient and Robust Discrete Conformal Equivalenc…
We give a general criterion for the Dirichlet problem at infinity (DPI) on a Cartan-Hadamard surface to be solvable, which we primarily use to give the best possible upper radial radial curvature bound for solvability of the DPI, but which…
We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate…
Any surface is completely characterized by a metric and a symmetric tensor satisfying the Gauss-Codazzi-Mainardi equations (GCM), which identifies the latter as its curvature. We demonstrate that physical questions relating to a surface…
For a surface immersed in a three-dimensional space endowed with a norm instead of an inner product, one can define analogous concepts of curvature and metric. With these concepts in mind, various questions immediately appear. The aim of…
Let $\Omega$ be a bounded domain of $\mathbb{R}^3$ whose closure $\overline{\Omega}$ is polyhedral, and let $\mathcal{T}$ be a triangulation of $\overline{\Omega}$. Assuming that the boundary of $\Omega$ is sufficiently regular, we provide…
We study the properties of $\text{CAT}(\kappa)$ surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the $\text{CAT}(\kappa)$ condition locally. The main facts about…
In this paper, we propose a novel parameterization method for genus-one and multiply connected genus-zero surfaces, called periodic conformal flattening. The conformal energy minimization technique is utilized to compute the desired…
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal…
This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…
On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
In clinical applications, the utility of segmentation models is often based on the accuracy of derived downstream metrics such as organ size, rather than by the pixel-level accuracy of the segmentation masks themselves. Thus, uncertainty…
Weighted Gaussian Curvature is an important measurement for images. However, its conventional computation scheme has low performance, low accuracy and requires that the input image must be second order differentiable. To tackle these three…
Topology and geometry are deeply intertwined in the study of surfaces, though their interaction manifests differently in smooth and discrete settings. In the smooth category, a classical result asserts that any closed smooth surface…
Given a smooth compact manifold with boundary, we study variational properties of the volume functional and of the area functional of the boundary, restricted to the space of the Riemannian metrics with prescribed curvature. We obtain a…
This paper is concerned with the problem of prescribing Gaussian curvature and geodesic curvature in a compact surface with boundary with conical singularities and corners. Solutions are obtained using a new variational formulation,…
In this investigation we revisit the concept of "effective free surfaces" arising in the solution of the time-averaged fluid dynamics equations in the presence of free boundaries. This work is motivated by applications of the optimization…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…
We propose a template-driven triangulation framework that embeds raster- or segmentation-derived boundaries into a regular triangular grid for stable PDE discretization on image-derived domains. Unlike constrained Delaunay triangulation…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…