Affine invariant points and new constructions

详细信息    查看全文

• 作者：Ivan Iurchenko ^{iurchenk@ualberta.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Affine invariant points ; Symmetry ; Convex geometry
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1410-1416
• 全文大小：257 K

文摘

In [2] Grünbaum asked if the set of all affine invariant points of a given convex body is equal to the set of all points invariant under every affine automorphism of the body. In [3] we have proven the case of a body with no nontrivial affine automorphisms. After some partial results  and  the problem was solved in positive by Mordhorst [8]. In this note we provide an alternative proof of the affirmative answer, developing the ideas of [3]. Moreover, our approach allows us to construct a new large class of affine invariant points.