Quasihyperbolic geodesics in convex domains
نویسنده
چکیده
We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesics are quasiconvex in the norm metric in convex domains in all normed spaces. 2000 Mathematics Subject Classification: 30C65
منابع مشابه
The Quasihyperbolic Metric and Associated Estimates on the Hyperbolic Metric
In this paper we investigate the geometry of the quasihyperbolic metric of domains in R". This metric arises from the conformally flat generalized Riemannian metric d(x, aD)' ldx I. Due to the fact that the density cl(x, aD) -t is not necessarily differentiable, the classical theories of Riemannian geometry do not apply to this metric. The quasihyperbolic metric has been found to have many inte...
متن کاملQuasihyperbolic geometry of domains in Hilbert spaces
The paper deals with basic smoothness and bilipschitz properties of geodesics, balls and spheres in the quasihyperbolic metric of a domain in a Hilbert space. 2000 Mathematics Subject Classification: 30C65
متن کاملComplex Geodesics on Convex Domains
Existence and uniqueness of complex geodesics joining two points of a convex bounded domain in a Banach space X are considered. Existence is proved for the unit ball of X under the assumption that X is 1-complemented in its double dual. Another existence result for taut domains is also proved. Uniqueness is proved for strictly convex bounded domains in spaces with the analytic Radon-Nikodym pro...
متن کاملConvexity and Geodesic Metric Spaces
In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...
متن کاملUniversal Convexity for Quasihyperbolic Type Metrics
We characterize the open sets in the sphere that are geodesically convex in any containing domain with respect to various conformal metrics.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005