论文标题
Minkowski型定理用于锥体中的凸集
Minkowski type theorems for convex sets in cones
论文作者
论文摘要
Minkowski的经典存在定理为欧几里得空间的单位球体上的Borel度量提供了必要和足够的条件，使其成为凸体的表面积测量。该解决方案是独特的，直到翻译为单位。我们处理无界凸集的相应问题，其无限源的行为由给定的封闭凸锥确定。我们提供存在定理和稳定性结果。
Minkowski's classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface area measure of a convex body. The solution is unique up to a translation. We deal with corresponding questions for unbounded convex sets, whose behavior at infinity is determined by a given closed convex cone. We provide an existence theorem and a stability result.
