Characterizing complete $\operatorname{CAT}(\kappa)$-spaces, $\kappa<0$, with geodesic boundary
نویسندگان
چکیده
منابع مشابه
Convexity 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 کاملSmall Hyperbolic 3-Manifolds With Geodesic Boundary
We classify the orientable finite-volume hyperbolic 3-manifolds having nonempty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. We also compute the volume of all such manifolds, we describe their canonical Kojima decomposition, and we discuss manifolds having cusps. The manifolds built from one or two tetrahedra were previously known. There a...
متن کاملCommensurability of hyperbolic manifolds with geodesic boundary
Suppose n > 3, let M1,M2 be n-dimensional connected complete finitevolume hyperbolic manifolds with non-empty geodesic boundary, and suppose that π1(M1) is quasi-isometric to π1(M2) (with respect to the word metric). Also suppose that if n = 3, then ∂M1 and ∂M2 are compact. We show that M1 is commensurable with M2. Moreover, we show that there exist homotopically equivalent hyperbolic 3-manifol...
متن کاملProximinality in Geodesic Spaces
Let X be a complete CAT(0) space with the geodesic extension property and Alexandrov curvature bounded below. It is shown that if C is a closed subset of X , then the set of points of X which have a unique nearest point in C is Gδ and of the second Baire category inX. If, in addition,C is bounded, then the set of points ofX which have a unique farthest point in C is dense in X. A proximity resu...
متن کاملComplete Shape Metric and Geodesic
We develop the framework for moving domain and geometry under minimal regularity (of moving boundaries). This question arose in shape control analysis and non cylindrical PDE analysis. We apply here this setting to the morphic measure between shape or images. We consider both regular and non smooth situations and we derive complete shape metric space with characterization of geodesic as being s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2010-05144-x