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Статьи
Affine hemispheres of elliptic type
B. Klartagab a Department of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel
b School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Аннотация:
We find that for any
$n$-dimensional, compact, convex set
$K\subseteq\mathbb R^{n+1}$ there is an affinely-spherical hypersurface
$M\subseteq\mathbb R^{n+1}$ with center in the relative interior of
$K$ such that the disjoint union
$M\cup K$ is the boundary of an
$(n+1)$-dimensional, compact, convex set. This so-called affine hemisphere
$M$ is uniquely determined by
$K$ up to affine transformations, it is of elliptic type, is associated with
$K$ in an affinely-invariant manner, and it is centered at the Santaló point of
$K$.
Ключевые слова:
affine sphere, cone measure, anchor, Santaló point, obverse.
Поступила в редакцию: 13.12.2015
Язык публикации: английский
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