𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Total curvature and length estimate for curves in CAT(K) spaces

✍ Scribed by Chaiwat Maneesawarng; Yongwimon Lenbury


Book ID
104358216
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
141 KB
Volume
19
Category
Article
ISSN
0926-2245

No coin nor oath required. For personal study only.

✦ Synopsis


We introduce the notion of total curvature of curves (which agrees with the usual one in the piecewise smooth case) in spaces of Alexandrov curvature bounded above. Basic properties of total curvature, including rectifiability of curves of finite total curvature and additivity of total curvature, are then obtained. A sharp upper estimate of a type due to Schmidt on the length of a curve in a CAT(K) space is also given in terms of its total curvature and the distance between its endpoints.


πŸ“œ SIMILAR VOLUMES