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The growth rate of surface area measure for noncompact convex sets with prescribed asymptotic cone
Vadim Semenov, Yiming Zhao
Source abstract
The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Ampère equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and sufficient condition for existence and uniqueness) in dimension 2 is presented. In higher dimensions, partial results are demonstrated.
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