A Discrete Blaschke Theorem for Convex Polygons in 2-Dimensional Space Forms
Let $M$ be a $2$-dimensional 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 prove the following Blaschke-type theorem: “If $P$ is a convex polygon in $M$ with curvature at its vertices $\kapp...
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| Datum: | 2024 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1067 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | Let $M$ be a $2$-dimensional 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 prove the following Blaschke-type theorem: “If $P$ is a convex polygon in $M$ with curvature at its vertices $\kappa _i\ge \kappa _0 >0$, then the circumradius $R$ of $P$ satisfies $\textrm{ta}_\lambda(R) \le \pi/(2\kappa _0)$ and the equality holds if and only if the polygon is a doubly covered segment”.
Mathematical Subject Classification 2020: 52A10, 52A55, 51M10, 53C22 |
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