— The morphology of vesicles with topological genus g = 2 is studied using the properties of Willmore surfaces together with the conformal invariance of the bending energy of fluid membranes. In the phase diagram of the bilayer couple model, a region exists where vesicle shapes are given by Willmore surfaces. Within this region, shapes in general have no mirror symmetries and the ground state i...

Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new ac...

Let f, g : Mn → Rn+d be two immersions of an n-dimensional differentiable manifold into Euclidean space. That g is conformal (isometric) to f means that the metrics induced on Mn by f and g are conformal (isometric). We say that f is conformally (isometrically) rigid if given any other conformal (isometric) immersion g there exists a conformal (isometric) diffeomorphism Υ from an open subset of...

the years 1895 to 1898 were momentous for their impact on health and human well beings. first, wilhelm roentgen noted a glowing fluorescent screen, caused by invisible rays. this event subsequently led to the discovery of x-rays in 1895, and thus the birth of the “atomic age”. next becquerel’s investigations of these mysterious rays led to his experiments with uranium salt crystals. he thought ...

We consider the question: can the isotropy representation of an irreducible pseudoRiemannian symmetric space be realized as a conformal holonomy group? Using recent results of Čap, Gover and Hammerl, we study the representations of SO(2, 1), PSU(2, 1) and PSp(2, 1) as isotropy groups of irreducible symmetric spaces of signature (3, 2), (4, 4) and (6, 8), respectively, describing the geometry in...

Cortical flattening algorithms are becoming more widely used to assist in visualizing the convoluted cortical gray matter sheet of the brain. Metric-based approaches are the most common but suffer from high distortions. Conformal, or angle-based algorithms, are supported by a comprehensive mathematical theory. The conformal approach that uses circle packings is versatile in the manipulation and...

Conformal algebra on R × S derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess-Zumino action managing non-perturbative dynamics of the conformal factor in the metric field. It is shown that the residual diff...

In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal modules over the Virasoro and the N=1 Neveu-Schwarz algebras, and over the current algebras. 0. Introduction Conformal module is a basic tool for the construction of free field realization of infini...

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...