A weighted Minkowski theorem for pseudo-cones

Abstract: A nonempty closed convex set in , not containing the origin, is called a pseudo-cone if with every x it also contains λx for . We consider pseudo-cones with a given recession cone C, called C-pseudo-cones. The family of C-pseudo-cones can, with reasonable justification, be considered as a counterpart to the family of convex bodies containing the origin in the interior. For a C-pseudo-cone one can naturally define a surface area measure and a covolume. Since they are in general infinite, we introduce a weighting, leading to modified versions of surface area and covolume. These are finite and still homogeneous, though of other degrees. Our main result is a Minkowski type existence theorem for C-pseudo-cones with given weighted surface area measure

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Advances in mathematics. - 450 (2024) , 109760, ISSN: 1090-2082

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2024
• Creator: Schneider, Rolf

Further information

• DOI: 10.1016/j.aim.2024.109760
• URN: urn:nbn:de:bsz:25-freidok-2515416
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 11:03 AM CEST