WEIGHTED CONE-VOLUME MEASURES OF PSEUDO-CONES  

作　　者：Rolf SCHNEIDER 

机构地区：[1]Mathematisches Institut,Albert–Ludwigs-Universität,D-79104,Freiburg i.Br.,Germany

出　　处：《Acta Mathematica Scientia》2025年第1期40-51,共12页数学物理学报(B辑英文版)

摘　　要：A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.

关 键 词：pseudo-cone surface area measure cone-volume measure weighting Minkowski type problem 

分 类 号：O17[理学—数学]