Search results for " Topology"
showing 10 items of 1371 documents
Fractional Maximal Functions in Metric Measure Spaces
2013
Abstract We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.
Two‐dimensional metric spheres from gluing hemispheres
2022
We study metric spheres (Z,dZ) obtained by gluing two hemispheres of S2 along an orientation-preserving homeomorphism g:S1→S1, where dZ is the canonical distance that is locally isometric to S2 off the seam. We show that if (Z,dZ) is quasiconformally equivalent to S2, in the geometric sense, then g is a welding homeomorphism with conformally removable welding curves. We also show that g is bi-Lipschitz if and only if (Z,dZ) has a 1-quasiconformal parametrization whose Jacobian is comparable to the Jacobian of a quasiconformal mapping h:S2→S2. Furthermore, we show that if g−1 is absolutely continuous and g admits a homeomorphic extension with exponentially integrable distortion, then (Z,dZ) …
Sobolev homeomorphic extensions onto John domains
2020
Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous $W^{1,2}$-extension but not even a homeomorphic $W^{1,1}$-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents $p<2$. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.
A note on some fundamental results in complete gauge spaces and application
2015
We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.
Pants complex, TQFT and hyperbolic geometry
2021
We present a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the curve operators in the skein theoretic version of the $SU(2)$-TQFT, as developed by Blanchet, Habegger, Masbaum and Vogel, we define the quantum intersection number between pants decompositions of a closed surface. We show that the quantum intersection number admits two sided bounds in terms of the geometric intersection number and we use it to obtain a metric on the pants graph of surfaces. Using work of Brock we show that the pants graph equipped with this …
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
2003
We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every right-angled Artin group can be embedded in a pure surface braid group. On the other hand, by generalising to right-angled Artin groups a result of Lyndon for free groups, we show that the Euler characteristic -1 surface group (given by the relation x^2y^2=z^2) never embeds in a right-angled Artin group.
Approach to the Design of Transmission-Type Injection-Locked Microwave Oscillators through Behavioral Block Modeling
2010
In this work, an attempt is made toward the development of a systematic design method for the performance- driven dimensioning of the various elements comprising the structure of modern transistor-based microwave injection- locked oscillators with transmission-type topologies (TILOs). The proposed approach is based on the use of appropriate diakoptics of the various circuit blocks into a matched environment, and their behavioral modeling in the fundamental- frequency dynamical complex envelope domain with the help of standard circuit and E.M. simulation CAD tools. This will permit, in the end, to obtain closed-form expressions for the main TILO performances in terms of the design parameters…
Prediction of properties of chiral compounds by molecular topology
1998
Abstract A common assumption in chemistry is that chiral behavior is associated with 3-D geometry. However, chiral information is related to symmetry, which allows the topological handling of chiral atoms by weighted graphs and the calculation of new descriptors that give a weight to the corresponding entry in the main diagonal of the topological matrix. In this study, it is demonstrated that, operating in this way, chiral topological indices are obtained that can differentiate the pharmacological activity between pairs of enantiomers. The 50% inhibitory concentration (IC50) values of the D2 dopamine receptor and the σ receptor for a group of 3-hydroxy phenyl piperidines are specifically pr…
Unique continuation results for certain generalized ray transforms of symmetric tensor fields
2022
Let $I_{m}$ denote the Euclidean ray transform acting on compactly supported symmetric $m$-tensor field distributions $f$, and $I_{m}^{*}$ be its formal $L^2$ adjoint. We study a unique continuation result for the normal operator $N_{m}=I_{m}^{*}I_{m}$. More precisely, we show that if $N_{m}$ vanishes to infinite order at a point $x_0$ and if the Saint-Venant operator $W$ acting on $f$ vanishes on an open set containing $x_0$, then $f$ is a potential tensor field. This generalizes two recent works of Ilmavirta and M\"onkk\"onen who proved such unique continuation results for the ray transform of functions and vector fields/1-forms. One of the main contributions of this work is identifying t…