REGULARITY AND EXTREMALITY OF QUASICONFORMAL HOMEOMORPHISMS ON CR 3-MANIFOLDS
作者： Puqi Tang
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摘要: This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex Cauchy-Riemann manifolds. Then moduli curve families are used to estimate maximal dilatations quasiconformal homeomorphisms. On certain CR 3-manifolds, namely, circle bundles over flat tori, extremal ho- meomorphisms in some homotopy classes constructed. These mappings have similar behavior Teichmuller Riemann surfaces.
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acadsci.fi 参考文章(9)
Adam Korányi, Hans Martin Reimann, Quasiconformal mappings on CR manifolds Springer, Berlin, Heidelberg. pp. 59- 75 ,(1990) , 10.1007/BFB0089405
Robert S. Strichartz, Sub-Riemannian geometry Journal of Differential Geometry. ,vol. 24, pp. 221- 263 ,(1986) , 10.4310/JDG/1214440436
Oswald Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale Akademie der Wissenschaften , In Kommission bei W. de Gruyter. ,(1940)
Jussi Väisälä, Lectures on n-Dimensional Quasiconformal Mappings ,(1971)
Ursula Hamenstädt, Some regularity theorems for Carnot-Carathéodory metrics Journal of Differential Geometry. ,vol. 32, pp. 819- 850 ,(1990) , 10.4310/JDG/1214445536
Walter Rudin, Real and complex analysis ,(1966)
S I Pinchuk, Sh I Tsyganov, THE SMOOTHNESS OF CR-MAPPINGS BETWEEN STRICTLY PSEUDOCONVEX HYPERSURFACES Mathematics of The Ussr-izvestiya. ,vol. 35, pp. 457- 467 ,(1990) , 10.1070/IM1990V035N02ABEH000714
A. Kor�nyi, H. M. Reimann, Quasiconformal mappings on the Heisenberg group Inventiones Mathematicae. ,vol. 80, pp. 309- 338 ,(1985) , 10.1007/BF01388609
L{ászl{ó Lempert, On three-dimensional Cauchy-Riemann manifolds Journal of the American Mathematical Society. ,vol. 5, pp. 923- 969 ,(1992) , 10.1090/S0894-0347-1992-1157290-3