Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
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Publication:2537509
DOI10.1007/BF02684590zbMath0189.09402OpenAlexW2079500737WikidataQ59411260 ScholiaQ59411260MaRDI QIDQ2537509
Publication date: 1968
Published in: Publications Mathématiques (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=PMIHES_1968__34__53_0
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geodesic flows on symmetric Riemann spaces
- Density properties for certain subgroups of semi-simple groups without compact components
- Homogeneous spaces with finite invariant measure
- Su una teoria generale della misura \((r-1)\)-dimensionale in uno spazio ad \(r\) dimensioni
- On quasiconformal mappings
- On Quasi-Conformality and Pseudo-Analyticity
- Curvature Measures
- Symmetrization of Rings in Space
- A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
- Rings and Quasiconformal Mappings in Space