We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces obtained from range scanners often have holes or missing regions where the 3D models are incomplete. In order to analyze the 3D shapes effectively, restoring the incomplete shape by filling in the surface holes is neces...

We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establi...

The goal of this paper is to express the Bach tensor of a four– dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach t...

We take advantage of the Shiromizu et al. covariant formalism to find out brane properties originating from five dimensional bulk spacetime. Making a different choice for conformal factor $e^{-2b(z)}$ compared Estrada [24], we reach new solution with lot interesting properties, where $b(z) = ln(1/\sqrt{cosh2\mu z})$. The non-local tensor $E_{ab}$ rooted 5-dimensional Riemann gives an anisotropi...

The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in the quantum corrections; depending on the values of quantization parameters, they obey an exact or perturbed power-law expansion in conformal time. The comov...

A method which uses a generalized ζ-function to compute the renormalized (Euclidean) stress tensor of a quantum field propagating in a curved background is presented. The method does not use point-splitting procedures or off-diagonal ζ functions but employs an analytic continuation of a generalized ζ-function. The starting point of the method is the direct computation of the functional derivati...

Representation and comparison of shapes is a problem with many applications in computer vision and imaging, including object recognition and medical diagnosis. We will discuss some constructions from the theory of conformal mapping which provide ways to represent and compare planar shapes. It is a remarkable fact that conformal maps from the unit disk to a planar domain encode the geometry of t...

Recall that a conformal 4-manifold is called self-dual if its Weyl curvature, considered as a bundle valued 2-form, is in the +1 eigenspace of the Hodge star-operator [1]. Due to Schoen’s proof [19] of the Yamabe conjecture it is known that within any conformal class on a compact manifold is a metric whose scalar curvature is constant and the sign of this constant is a conformal invariant. The ...

Given two two-dimensional conformal field theories, a domain wall – or defect line – between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and...

We show that the Plebanski-Demianski spacetime persists as a solution of General Relativity when theory is supplemented with both, conformally coupled scalar and quadratic curvature corrections. The terms are two types given by combinations Riemann tensor well higher interaction constructed field which to in curvature. later built four-rank $S_{\mu\nu}^{\ \ \lambda\rho}$ depends on field, trans...