תקציר
We give an affirmative answer to a question asked by Gardner and Mauldin (Geom. Dedicata 26, 323-332, 1988) about bijections of the plane taking each polygon with n sides onto a polygon with n sides. We also state and prove more general results in this spirit. For example, we show that an injective mapping taking each convex n-gon onto a non-degenerate n-gon (not necessarily convex or even simple) must be affine.
| שפה מקורית | אנגלית |
|---|---|
| כותר פרסום המארח | Asymptotic Geometric Analysis |
| כותר משנה של פרסום המארח | Proceedings of the Fall 2010 Fields Institute Thematic Program |
| עורכים | Monika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann |
| עמודים | 299-312 |
| מספר עמודים | 14 |
| מזהי עצם דיגיטלי (DOIs) | |
| סטטוס פרסום | פורסם - 2013 |
| פורסם באופן חיצוני | כן |
סדרות פרסומים
| שם | Fields Institute Communications |
|---|---|
| כרך | 68 |
| ISSN (מודפס) | 1069-5265 |
הערה ביבליוגרפית
Funding Information:The author would like to thank his advisor, Prof. Shiri Artstein–Avidan, for bringing the problems presented in [] to his attention and for fruitful discussions. The author would also like to thank the anonymous referee for numerous helpful comments. This work has been partially supported by ISF grant No. 247/11.