Related papers: Opening nodes and the DPW method
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…
We investigate the close relationship between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. Just as in the case of minimal surfaces in Euclidean 3-space, the only complete connected…
In this paper we address the issue of designing developable surfaces with Bezier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumann's…
We introduce a novel learning-based, visibility-aware, surface reconstruction method for large-scale, defect-laden point clouds. Our approach can cope with the scale and variety of point cloud defects encountered in real-life Multi-View…
Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…
We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the…
Author reduces the Minkowski problem to the problem of construction the G-deformations preserving the product of principal curvatures for every point of surface in Riemannian space. G-deformation transfers every normal vector of surface in…
This work outlines a new three-dimensional diffuse interface finite volume method for the simulation of multiple solid and fluid components featuring large deformations, sliding and void opening. This is achieved by extending an existing…
For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with punctures.
We carry out the first main step towards the construction of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of self-similar surfaces and…
It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. If a slope on the boundary of the link-manifold is…
Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.
We enlarge the class of open Riemann surfaces known to be holomorphically embeddable into the plane by allowing them to have additional isolated punctures compared to the known embedding results.
We start the investigation of immersions $\Psi$ of a simply connected domain $D$ into three dimensional Euclidean space $R^3$, which have constant mean curvature (CMC-immersions), and allow for a group of automorphisms of $D$ which leave…
This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by…
We prove the existence of embedded closed constant curvature curves on convex surfaces.
In earlier work of NK new closed embedded smooth minimal surfaces in the round three-sphere $\mathbb{S}^3(1)$ were constructed, each resembling two parallel copies of the equatorial two-sphere $\mathbb{S}^2_{eq}$ joined by small catenoidal…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…