Title: A discrete Blaschke Theorem for convex polygons in $2$-dimensional space
forms
Authors: Alexander Borisenko and Vicente Miquel
Categories: math.DG
Comments: 11 pages, 2 figures
MSC-class: 52A10, 52B99, 53C20
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Let $M$ be a $2$-space form. Let $P$ be a convex polygon in $M$. For these
polygons, we define (and justify) a curvature $\kappa_i$ at each vertex $A_i$
of the polygon and and prove the following Blaschke’s type theorem: If $P$ is a
convex plygon in $M$ with curvature at its vertices $\kappa_i\ge \kappa_0 >0$,
then the circumradius $R$ of $P$ satisfies $ta_\lambda(R) \le \pi/(2\kappa_0)$
and the equality holds if and only if the polygon is a $2$-covered segment.
\\ ( https://arxiv.org/abs/2305.07566 , 62kb)