Search results for "mapping"

Quasiconformal maps in metric spaces with controlled geometry

1998

This paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry. The principal message is that such a theory is both relevant and viable. The first main issue is the problem of definition, which we next describe. Quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount. This requirement makes sense in every metric space. Given a homeomorphism f from a metric space X to a metric space Y , then for x∈X and r>0 set

Asymptotic values and hölder continuity of quasiconformal mappings

1987

Cone conditions and quasiconformal mappings

1988

Let f be a quasiconformal mapping of the open unit ball B n = {x ∈ R n : | x | < l× in euclidean n-space R n onto a bounded domain D in that space. For dimension n= 2 the literature of geometric function theory abounds in results that correlate distinctive geometric properties of the domain D with special behavior, be it qualitative or quantitative, on the part of f or its inverse. There is a more modest, albeit growing, body of work that attempts to duplicate in dimensions three and above, where far fewer analytical tools are at a researcher’s disposal, some of the successes achieved in the plane along such lines. In this paper we contribute to that higher dimensional theory some observati…

Distortion of quasiconformal maps in terms of the quasihyperbolic metric

2013

Abstract We extend a theorem of Gehring and Osgood from 1979–relating to the distortion of the quasihyperbolic metric by a quasiconformal mapping between Euclidean domains–to the setting of metric measure spaces of Q -bounded geometry. When the underlying target space is bounded, we require that the boundary of the image has at least two points. We show that even in the manifold setting, this additional assumption is necessary.

Quasiconformal mappings and global integrability of the derivative

1991

Quasiextremal distance domains and extension of quasiconformal mappings

1985

Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings

2001

We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.

Differential associations of age with volume and microstructure of hippocampal subfields in healthy older adults

2015

Hippocampal atrophy in advanced healthy aging has frequently been reported. However, the vulnerability of different hippocampal subfields to age-related atrophy is still a source of debate. Moreover, the association of age with the microstructural integrity of subfields is largely unknown. In this study, we investigated the associations between age and volume as well as microstructural integrity of hippocampal subfields using a three-dimensional (3D) surface mapping approach. Forty-three healthy older adults spanning the age range from 60 to 85 years underwent T1-weighted and diffusion-tensor imaging. Analyses demonstrated an association of age with hippocampal volume predominantly in the m…

Some notes on a second-order random boundary value problem

2017

We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution.

The yeast putative transcriptional repressor RGM1 is a proline-rich zinc finger protein.

1991

Abstract I have cloned a yeast gene, RGM1, which encodes a proline-rich zinc, finger protein. rgm1 mutants do not show any obvious phenotype but overexpression of RGM1 gene greatly impairs cell growth. The proline-rich region of RGM1 attached to a heterologous DNA binding domain is able to repress the expression of the target gene. RGM1 shares similar zinc finger motifs with the mammalian Egr (early growth response) proteins as well as proline-rich sequences with a high serine and threonine content, suggesting that RGM1 and Egr proteins could have functional similarities.