Isometric embedding of Busemann surfaces into L1
نویسندگان
چکیده
In this note, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into L1. As a corollary, we obtain that all planar graphs which are 1skeletons of planar non-positively curved complexes with regular Euclidean polygons as cells are L1-embeddable with distortion at most 2 + π/2 < 4. Our results significantly improve and simplify the results of the recent paper A. Sidiropoulos, Non-positive curvature, and the planar embedding conjecture, FOCS 2013.
منابع مشابه
Isometric Embedding of Facial Surfaces into S3
The problem of isometry-invariant representation and comparison of surfaces is of cardinal importance in pattern recognition applications dealing with deformable objects. Particularly, in threedimensional face recognition treating facial expressions as isometries of the facial surface allows to perform robust recognition insensitive to expressions. Isometry-invariant representation of surfaces ...
متن کاملInto isometries that preserve finite dimensional structure of the range
In this paper we study linear into isometries of non-reflexive spaces (embeddings) that preserve finite dimensional structure of the range space. We consider this for various aspects of the finite dimensional structure, covering the recent notion of an almost isometric ideals introduced by Abrahamsen et.al., the well studied notions of a M -ideal and that of an ideal. We show that if a separabl...
متن کاملA Banach Subspace of L 1 / 2 Which Does Not Embed In
For every n ≥ 3, we construct an n-dimensional Banach space which is isometric to a subspace of L1/2 but is not isometric to a subspace of L1. The isomorphic version of this problem (posed by S. Kwapien in 1969) is still open. Another example gives a Banach subspace of L1/4 which does not embed isometrically in L1/2. Note that, from the isomorphic point of view, all the spaces Lq with q < 1 hav...
متن کاملThe Energy of Equivariant Maps and a Fixed-point Property for Busemann Nonpositive Curvature Spaces
For an isometric action of a finitely generated group on the ultralimit of a sequence of global Busemann nonpositive curvature spaces, we state a sufficient condition for the existence of a fixed point of the action in terms of the energy of equivariant maps from the group into the space. Furthermore, we show that this energy condition holds for every isometric action of a finitely generated gr...
متن کاملAffine Isometric Embedding for Surfaces
A strictly convex hypersurface in Rn can be endowed with a Riemannian metric in a way that is invariant under the group of (equi)affine motions. We study the corresponding isometric embedding problem for surfaces in R3. This problem is formulated in terms of a quasilinear elliptic system of PDE for the Pick form. A negative result is obtained by attempting to invert about the standard embedding...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 53 شماره
صفحات -
تاریخ انتشار 2015