Title: A discrete Blaschke Theorem for convex polygons in $2$-dimensional space
\n forms
\nAuthors: Alexander Borisenko and Vicente Miquel
\nCategories: math.DG
\nComments: 11 pages, 2 figures
\nMSC-class: 52A10, 52B99, 53C20
\n\\\\
\n Let $M$ be a $2$-space form. Let $P$ be a convex polygon in $M$. For these
\npolygons, we define (and justify) a curvature $\\kappa_i$ at each vertex $A_i$
\nof the polygon and and prove the following Blaschke’s type theorem: If $P$ is a
\nconvex plygon in $M$ with curvature at its vertices $\\kappa_i\\ge \\kappa_0 >0$,
\nthen the circumradius $R$ of $P$ satisfies $ta_\\lambda(R) \\le \\pi\/(2\\kappa_0)$
\nand the equality holds if and only if the polygon is a $2$-covered segment.
\n\\\\ ( https:\/\/arxiv.org\/abs\/2305.07566 , 62kb)<\/p>\n","protected":false},"excerpt":{"rendered":"