On absolutely conformal mappings

• Autores: David Kalaj, Miodrag Mateljevic
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 77, Fasc. 1-2, 2010, págs. 33-38
• Idioma: inglés
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• Resumen

  • Let ­ be a domain in Rn. It is proved that, if u 2 C1(­;Rn) and there holds the formula kru(x)kn = nn=2j detru(x)j in ­, then for n ¸ 3 u is a restriction of a MÄobius transformation, and for n = 2, u is an analytic function. This extends, partially, the well-known Liouville theorem ([?]), wich states that if u 2 ACLn(­;Rn), n ¸ 3, and the condition kru(x)kn = nn=2 detru(x) is satis¯ed a.e. in ­, then u is a restriction of a MÄobius transformation.