A uniqueness result for mean section bodies

作者：Goodey Paul^*; Weil Wolfgang

来源：Advances in Mathematics, 2012, 229(1): 596-601.

DOI：10.1016/j.aim.2011.09.009

• Convex bodies
• Surface area measures
• Mean section bodies

For 1 %26lt;= k %26lt;= d, the k-th mean section body, M-k (K), of a convex body K in R-d, is the Minkowski sum of all its sections by k-dimensional flats. We will show that, for any fixed 1 %26lt; k %26lt; d, the body K is uniquely determined by the body M k (K), assuming dim K %26gt;= d - k + 2. This result was previously known only for centrally symmetric bodies, or, in full generality, only for the case k = 2.

• 出版日期2012-1-15