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Discrete & Computational Geometry, ISSN 0179-5376, 9/2010, Volume 44, Issue 2, pp. 330 - 428
Journal Article
数学学报:英文版, ISSN 1439-8516, 2015, Volume 31, Issue 9, pp. 1424 - 1434
This paper studies the quasisymmetric mappings on Moran sets. We introduce a gener- alized form of weak quasisymmetry and prove that, on Moran set satisfying... 
小间隙 | 拟对称映射 | Moran集 | 一般化 | 30C65 | Quasisymmetric mapping | Moran sets | weakly quasisymmetric mapping | 28A80 | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | Studies | Mathematical analysis | Mapping | Criteria
Journal Article
Fractals, ISSN 0218-348X, 02/2018, Volume 26, Issue 1, p. 1850010
In this paper, we prove that a large class of homogeneous perfect sets of Hausdorff dimension 1 is quasisymmetrically Hausdorff minimal. We also obtain the... 
Hausdorff Dimension | Homogeneous Perfect Set | Quasisymmetric Mapping | Packing Dimension | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | CONFORMAL MAPPINGS | CANTOR SETS | MORAN SETS
Journal Article
Fractals, ISSN 0218-348X, 09/2019, Volume 27, Issue 6, p. 1950101
In this paper, we prove that a large class of Moran sets on the line with packing dimension 1 is quasisymmetrically packing-minimal. 
HAUSDORFF DIMENSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Quasisymmetric Mapping | Packing Dimension | Moran Set | MULTIDISCIPLINARY SCIENCES
Journal Article
International mathematics research notices, ISSN 1687-0247, 2018, Volume 2018, Issue 12, pp. 3769 - 3799
Abstract We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the... 
MATHEMATICS | ASSOUAD DIMENSION | Mathematics - Classical Analysis and ODEs
Journal Article
Mathematical Notes, ISSN 0001-4346, 7/2016, Volume 100, Issue 1, pp. 123 - 131
..., published in Matematicheskie Zametki, 2016, Vol. 100, No. 1, pp. 144–154. Quantum Calculus and Quasiconformal Mappings A. G. Sergeev * Steklov Mathematical Institute... 
Mathematics, general | Connes quantization | Mathematics | quasisymmetric homeomorphism | Sobolev space of half-differentiable functions | SPACE | MATHEMATICS
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 05/2017, Volume 58, Issue 3, pp. 373 - 381
We introduce the new class of Jordan arcs (curves) of bounded rotation which includes all arcs (curves) of bounded turning. We prove that if the boundary of a... 
curve of bounded rotation | curve of bounded turning | Rickman criterion | quasimöbius mapping | quasiconformal extension | quasiconformal mapping | quasisymmetric mapping | MATHEMATICS | BOUNDARY CORRESPONDENCE | quasimobius mapping
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2017, Volume 42, Issue 2, pp. 575 - 584
We prove that an injection from the integer set into the real line admits a quasi-conformal extension to the complex plane if and only if it is quasisymmetric. 
Quasiconformal mapping | Quasisymmetric mapping | MATHEMATICS | quasisymmetric mapping
Journal Article
ANALYSIS AND MATHEMATICAL PHYSICS, ISSN 1664-2368, 12/2019, Volume 9, Issue 4, pp. 1941 - 1975
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 2, pp. 1400 - 1409
This paper studies the equivalence of the quasisymmetric mappings on non-connected sets... 
Weakly quasisymmetric mapping | Cantor-like sets | Quasisymmetric mapping | HAUSDORFF DIMENSION | MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL MAPPINGS | MORAN SETS
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2013, Volume 38, Issue 1, pp. 535 - 546
.... In our main results, we prove that if a quasisymmetric mapping f of [0,1] maps a uniform Cantor set E onto a uniform Cantor set f (E... 
Uniform Cantor set | Doubling measure | Thin set | Fat set | Quasisymmetric mapping | doubling measure | thin set | HAUSDORFF DIMENSION | MATHEMATICS | UNIFORM CANTOR SETS | quasisymmetric mapping | fat set
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 9/2018, Volume 59, Issue 5, pp. 768 - 777
We continue studying the BAD class of multivalued mappings of Ptolemaic Möbius structures in the sense of Buyalo with controlled distortion of generalized angles... 
Ptolemaic space | Möbius structure | quasimöbius mapping | inversion metric | inversion space | Mathematics, general | Mathematics | uniformly perfect space | quasisymmetric mapping | HTB-space | MATHEMATICS | Mobius structure | quasimobius mapping
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2016, Volume 41, Issue 1, pp. 287 - 304
Given a quasisymmetric homeomorphism, we introduce the concept of quasisymmetric exponent and explore its relations to other conformal invariants. As a... 
Quasisymmetric exponent | Dilatation | Quasisymmetric homeomorphism | Modulus | QUADRILATERALS | MATHEMATICS | QUASIEXTREMAL DISTANCE DOMAINS | QED DOMAINS | EXTENSIONS | CONFORMAL INVARIANTS | dilatation | MAPPINGS | modulus | quasisymmetric exponent
Journal Article
Analysis and Geometry in Metric Spaces, ISSN 2299-3274, 05/2018, Volume 6, Issue 1, pp. 48 - 63
We give conditions under which a fiber-preserving quasisymmetric map between open subsets of fibered metric spaces is locally biLipschitz. We also show that a... 
22E25 | 53C17 | quasiconformal map | fibered space | quasisymmetric map | 30L10 | rigidity | Carnot group | MATHEMATICS | HEISENBERG-GROUP | CARNOT GROUPS | CONFORMAL MAPPINGS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2018, Volume 146, Issue 10, pp. 4255 - 4263
We introduce a complex Banach manifold structure on the space of normalized symmetric homeomorphisms on the real line. 
Symmetric homeomorphism | Quasiconformal mapping | Quasisymmetric homeomorphism | Beltrami coefficient | MATHEMATICS | symmetric homeomorphism | MATHEMATICS, APPLIED | MAPPINGS | BOUNDARY | quasiconformal mapping | TEICHMULLER-SPACES
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2015, Volume 40, Issue 1, pp. 305 - 320
.... In the last section we show our analytic definition of quasisymmetry is consistent with earlier notions of conformal mappings on the Grushin plane... 
Conformal | Grushin plane | Beltrami equation | Quasiconformal | Quasisymmetric | MATHEMATICS | quasisymmetric | quasiconformal | conformal
Journal Article
Canadian mathematical bulletin, ISSN 0008-4395, 06/2013, Volume 56, Issue 2, pp. 292 - 305
M. Hu and S. Wen considered quasisymmetrically minimal uniform Cantor sets of Hausdorff dimension 1, where at the $K$ -th set one removes from each interval... 
Hausdorff Dimension | Moran Set | Quasisymmetric | MATHEMATICS | quasisymmetric | QUASI-CONFORMAL MAPPINGS | Hausdorff dimension | Moran set
Journal Article
Applied Mathematics-A Journal of Chinese Universities, ISSN 1005-1031, 6/2010, Volume 25, Issue 2, pp. 217 - 226
The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the... 
Extremal quasiconformal mapping | 30C62 | Mathematics, general | substantial boundary point | Mathematics | 30C70 | Applications of Mathematics | Hamilton sequence | quasisymmetric mapping | Quasisymmetric mapping | Substantial boundary point | MATHEMATICS, APPLIED | MAPPINGS | APPROXIMATION CONDITION
Journal Article
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