The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry

• Autores: Kai-Seng Chou, Xu-Jia Wang
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 205, Nº 1, 2006, págs. 33-83
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.07.004
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• Resumen

  • The Lp-Minkowski problem introduced by Lutwak is solved for pn+1 in the smooth category. The relevant Monge¿Ampère equation (0.1) is solved for all p>1. The same equation for p<1 is also studied and solved for p(-n-1,1). When p=-n-1 the equation is interpreted as a Minkowski problem in centroaffine geometry. A Kazdan¿Warner-type obstruction for this problem is obtained.