Title

On local quadratic subconvexity of metrics and rectifiability of Bézier curves in CAT(K) spaces.

Authors

Maneesawarng, Chaiwat; Lenbury, Yongwimon

Abstract

We generalize the definition of Bézier curves (which agrees with the usual one in the Euclidean case) in CAT(K) spaces. Rectifiability -- a naturally-expected property of Bézier curves -- is proved in this general setting. In order to achieve this, an assertion weaker but similar to convexity of metrics of CAT(0) spaces is verified for general metric spaces of curvature bounded above.

Subjects

MATHEMATICAL proofs; CURVATURE; CONVEXITY spaces; MATRICES (Mathematics); EUCLIDEAN algorithm; MATHEMATICAL analysis

Publication

Nonlinear Studies, 2011, Vol 18, Issue 3, p437

ISSN

1359-8678

Publication type

Academic Journal