Related papers: On in-plane drill rotations for Cosserat surfaces

Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal…

We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvature under the condition that at least one of translating curves lies in a plane.

Let $M$ be a connected compact orientable surface, $f:M\to \mathbb{R}$ be a Morse function, and $h:M\to M$ be a diffeomorphism which preserves $f$ in the sense that $f\circ h = f$. We will show that if $h$ leaves invariant each regular…

It is well known that certain pairs of planar domains have the same spectra of the Laplacian operator. We prove that these domains are still isospectral for a wider class of physical problems, including the cases of heterogeneous drums and…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

A question whether sufficiently regular manifold automorphisms may have wandering domains with controlled geometry is answered in the negative for quasiconformal or smooth homeomorphisms of $n$-tori, $n\ge2$, and hyperbolic surfaces.…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…

We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.

We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…

We introduce the rotation unfolding of the folding map of a surface in $\mathbb{R}^3$, and investigate its $\mathcal{A}$-vesality. The rotation unfolding is a 2-parameter unfolding and can be considered as a subfamily of the folding family,…

The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously…

Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…

We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic…

At each point in an immersed surface in $\mathbb R^4$ there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. More recently, at the singular point of a corank 1 singular surface in…

We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing…

A smooth ruled surface in 4-space has only parabolic points or inflection points of real type. We show, by means of contact with transverse planes, that at a parabolic point, there exist two tangent directions determining two planes along…

We classify rotational surfaces in a normed 3-space with rotationally symmetric norm whose principal curvatures satisfy a linear relation.