Search results for "Conformal map"
showing 10 items of 125 documents
Bonnesenʼs inequality for John domains in Rn
2012
Abstract We prove sharp quantitative isoperimetric inequalities for John domains in R n . We show that the Bonnesen-style inequalities hold true in R n under the John domain assumption which rules out cusps. Our main tool is a proof of the isoperimetric inequality for symmetric domains which gives an explicit estimate for the isoperimetric deficit. We use the sharp quantitative inequalities proved in Fusco et al. (2008) [7] and Fuglede (1989) [4] to reduce our problem to symmetric domains.
Geometric rigidity of conformal matrices
2009
We provide a geometric rigidity estimate a la Friesecke-James-Muller for conformal matrices. Namely, we replace SO(n) by a arbitrary compact subset of conformal matrices, bounded away from 0 and invariant under SO(n), and rigid motions by Mobius transformations.
Sharpness of uniform continuity of quasiconformal mappings onto s-John domains
2017
We construct examples to show the sharpness of uniform continuity of quasiconformal mappings onto $s$-John domains. Our examples also give a negative answer to a prediction in [7].
Hardy-Orlicz Spaces of conformal densities
2014
We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.
Exceptional Sets for Quasiconformal Mappings in General Metric Spaces
2008
A theorem of Balogh, Koskela, and Rogovin states that in Ahlfors Q-regular metric spaces which support a p-Poincare inequality, , an exceptional set of -finite (Q−p)- dimensional Hausdorff measure can be taken in the definition of a quasiconformal mapping while retaining Sobolev regularity analogous to that of the Euclidean setting. Through examples, we show that the assumption of a Poincare inequality cannot be removed.
Analytic Properties of Quasiconformal Mappings Between Metric Spaces
2012
We survey recent developments in the theory of quasiconformal mappings between metric spaces. We examine the various weak definitions of quasiconformality, and give conditions under which they are all equal and imply the strong classical properties of quasiconformal mappings in Euclidean spaces. We also discuss function spaces preserved by quasiconformal mappings.
Solving the NLO BK equation in coordinate space
2016
We present results from a numerical solution of the next-to-leading order (NLO) BalitskyKovchegov (BK) equation in coordinate space in the large Nc limit. We show that the solution is not stable for initial conditions that are close to those used in phenomenological applications of the leading order equation. We identify the problematic terms in the NLO kernel as being related to large logarithms of a small parent dipole size, and also show that rewriting the equation in terms of the “conformal dipole” does not remove the problem. Our results qualitatively agree with expectations based on the behavior of the linear NLO BFKL equation.
Next-to-next-to-leading order prediction for the photon-to-pion transition form factor
2003
We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$-function in the so-called conformal scheme. The Wilson--coefficients appearing in the non-forward kinematics are then entirely determined from those of the polarized deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$-function, and discuss numerical predictions calculated in different kinemati…
The generation of the ϱ-resonance by QCD
1992
By showing that the imaginary part of a suitable QCD amplitude, after extrapolation up to the cut, exhibits indeed a prominent bump structure where the ϱ-resonance is expected to be, a rather direct indication for the generation of the ϱ-resonance by QCD is given. This is achieved by using a mathematically rigorous method of stable analytic extrapolation, based on the theory of maximally converging sequences of polynomials and the application of conformal mappings.
QCD generates the ϱ-resonance
1991
Abstract The question whether the asymptotic QCD amplitude contains potentially hadronic resonances is examined by a mathematically rigorous method, based on the theory of maximally converging sequences of polynomials and conformal mappings. It is shown that the extrapolated amplitude to the physical cut exhibits indeed a bump structure which corresponds to the ϱ-resonance.