Abstract
In the following Sects. 3.1 and 3.2, we present the most basic geometric properties of solutions to the Monge-Ampere equation that were used in Chap. 2 Good references for these sections include the books by Gutierrez [10] and Figalli [7], the survey papers by Trudinger and Wang [20], De Philippis and Figalli [6] and Liu and Wang [15].
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