相关论文: 3-dimensional methods in contact geometry

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

This paper studies distributed-parameter systems on Riemannian manifolds with respect to Stokes-Dirac structures in a language of contact geometry with fiber bundles. For the class where energy functionals are quadratic, it is shown that…

Some examples and basic properties of ultrametric spaces are briefly discussed.

We study the geometry and codes of quartic surfaces with many cusps. We apply Gr\"obner bases to find examples of various configurations of cusps on quartics.

Shape assembly composes complex shapes geometries by arranging simple part geometries and has wide applications in autonomous robotic assembly and CAD modeling. Existing works focus on geometry reasoning and neglect the actual physical…

This is a set of lecture notes introducing graduate students to the topic of Discontinuous Petrov-Galerkin (DPG) methods.

The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…

In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n+1)-dimensional contact manifold and the…

Posing high-contact interactions is challenging and time-consuming, with hand-object interactions being especially difficult due to the large number of degrees of freedom (DOF) of the hand and the fact that humans are experts at judging…

This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…

We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…

This tutorial describes the geometry and algorithms for generating line drawings from 3D models, focusing on occluding contours. The geometry of occluding contours on meshes and on smooth surfaces is described in detail, together with…

Superintegrable Hamiltonian systems describing the interactions among three point masses on a line have been described in [2]. Here, we show examples of how the approach of above can be extended to a higher number of particles on a line and…

We propose an adaptation of the notion of scaling symmetries for the case of Lie-Hamilton systems, allowing their subsequent reduction to contact Lie systems. As an illustration of the procedure, time-dependent frequency oscillators and…

We study the Erdos distance conjecture on the unit sphere in three dimensions using Fourier analytic methods.

We study contact terms of conserved currents and the energy-momentum tensor in three-dimensional quantum field theory. They are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are…

Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transformations with four- and five-dimensional Lie symmetry algebras,…

In the context of additive manufacturing we present a novel technique for direct slicing of a dilated or eroded volume, where the input volume boundary is a triangle mesh. Rather than computing a 3D model of the boundary of the dilated or…

Contact-based motion planning for manipulation, object exploration or balancing often requires finding sequences of fixed and sliding contacts and planning the transition from one contact in the environment to another. However, most…

This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof…