Related papers: Cartan ribbonization and a topological inspection

We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and…

The main purpose of this article is to demonstrate three techniques for proving algebraicity statements about circle packings. We give proofs of three related theorems: (1) that every finite simple planar graph is the contact graph of a…

We study the arc complex of a surface with marked points in the interior and on the boundary. We prove that the isomorphism type of the arc complex determines the topology of the underlying surface, and that in all but a few cases every…

We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on…

In this paper we give a geometric argument for bounding the diameter of a connected compact surface (with boundary) of arbitrary codimension in Euclidean space in terms of Topping's diameter bound for closed surfaces (without boundary). The…

In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to…

We prove a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modeled: a component of the adjoint representation of the first embeds in the adjoint representation of the second. Consequences…

The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are…

The first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties. Our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all…

This article introduces efficient and user-friendly tools for analyzing the intersection curve between a ringed torus and an irreducible quadric surface. Without loose of generality, it is assumed that the torus is centered at the origin,…

We describe an efficient algorithm to compute a conformally equivalent metric for a discrete surface, possibly with boundary, exhibiting prescribed Gaussian curvature at all interior vertices and prescribed geodesic curvature along the…

Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

This is an introductory text on the more topological aspects of contact geometry, written for the Handbook of Differential Geometry vol. 2. After discussing (and proving) some of the fundamental results of contact topology (neighbourhood…

The method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires…

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

Cartan-Hadamard manifold is a simply connected Riemannian manifold with non-positive sectional curvature. In this article, we have proved that a Cartan-Hadamard manifold satisfying steady gradient Ricci soliton with the integral condition…

We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…

We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form…

Motivated by a M\"obius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular M\"obius invariant…