3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a fam...

Crowding is an intrinsic problem of all numerical conformal mapping techniques. The distance between some of the prevertices of a Schwarz-Christoffel map to an elongated polygon is exponentially small in the aspect ratio of the elongation. We show that a simple change, no domain decomposition or change of canonical domain is needed, to the existing algorithms introduced by Trefethen [L.N. Trefe...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We examine the local conformal invariance (Weyl invariance) in tensor-scalar theories used in recently proposed con...

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satis...

3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

If the conformal holonomy group Hol(T) of a simply connected space with conformal structure of signature (2p−1, 2q−1) is reduced to U(p, q) then the conformal holonomy is already contained in the special unitary group SU(p, q). We present two different proofs of this statement, one using conformal tractor calculus and an alternative proof using Sparling’s characterisation of Fefferman metrics.

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures and the Hausdorr dimension of the limit set. With every parabolic system we associate an innnite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical featur...

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to describe in further detail the holonomy of the adapted Weyl connection on conformal products. 2000 Mathematics...