Related papers: Veering branched surfaces, surgeries, and geodesic…
For each natural number n, we construct an example of a graph manifold supporting at least n different Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction: we cut a geodesic flow…
A vertical exterior derivative is constructed that is needed for a graded Poisson structure on multisymplectic manifolds over nontrivial vector bundles. In addition, the properties of the Poisson bracket are proved and first examples are…
A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…
We consider triangulations of closed surfaces in which every vertex is incident to exactly $d$ edges. These triangulations can be identified with subgroups of the triangle group $\langle a,b,c\mid a^2,b^2,c^2,(ab)^3,(ac)^2,(bc)^d\rangle$…
This master thesis looks at the gradient flow of the length functional on embedded loops. The space of embedded loops is endowed with a scale structure so that the length functional becomes scale smooth. For certain underlying manifolds,…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
Given a surface $\Sigma$ equipped with a set $P$ of marked points, we consider the triangulations of $\Sigma$ with vertex set $P$. The flip-graph of $\Sigma$ whose vertices are these triangulations, and whose edges correspond to flipping…
Embedding fields provide a way of coupling a background structure to a theory while preserving diffeomorphism-invariance. Examples of such background structures include embedded submanifolds, such as branes; boundaries of local subregions,…
We present an algebraic approach to the watershed adapted to edge or node weighted graphs. Starting with the flooding adjunction, we introduce the flooding graphs, for which node and edge weights may be deduced one from the other. Each node…
In this paper, the general formulation for inextensible flows of curves on oriented surface in $\mathbb{R}^3 $ is investigated. The necessary and sufficient conditions for inextensible curve flow lying an oriented surface are expressed as a…
In the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we show that a geodesically complete hyperbolic surface is made up of its convex…
The generating functions of the Severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. Recently new proofs of this fact were given for…
Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
Here we study the behaviour of the horocyclic orbit of a vector on the unit tangent bundle of a geometrically infinite surface with variable negative curvature, when the corresponding geodesic ray is almost minimizing and the injectivity…
Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced…
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
There are many approaches to the classification of Morse functions and their gradient fields (Morse Fields) on 2-surfaces. This paper studies the gluings of quadrilaterals and the classification of topological surfaces obtained by gluing…
We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a…