An N-dimensional Space That Admits a Poincar E Inequality but Has No Manifold Points
نویسنده
چکیده
For each integer n 2 we construct a compact, geodesic, metric space X which has topological dimension n, is Ahlfors n-regular, satis es the Poincar e inequality, possesses IR as a unique tangent cone at Hn almost every point, but has no manifold points.
منابع مشابه
On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons
The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...
متن کاملScattering and Complete Integrability in Conformally Invariant Nonlinear Theories
We study conformally invariant nonlinear wave equations in four dimensions corresponding to multicomponent massless scalar elds with a quartic interaction. We prove that the scattering operator S on the space H of nite-Einstein-energy Cauchy data has innnitely many xed points, as well as periodic points of all orders. There are also 2 H such that S n is almost periodic but not periodic, and 2 H...
متن کاملSimplicial Manifolds, Bistellar Flips and a 16-Vertex Triangulation of the Poincaré Homology 3-Sphere
We present an algorithm based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of the Poincar e homology 3-sphere; we construct an innnite series of non-P L d-dimensional spheres with d+13 vertices for d 5; and we show that if a d-manifold admits any triangulation on n vertices,...
متن کاملA New Poincar E Type Inequality
Using the Green's function and some comparison theorems, we obtain a lower bound on the rst Dirichlet eigenvalue for a domain D on a complete manifold with curvature bounded from above. And the lower bound is given explicitly in terms of the diameter of D and the dimension of D. This result can be considered as an analogue for nonpositively curved manifolds of Li-Schoen L-Sc] and Li-Yau's L-Ya]...
متن کاملNonexpansive mappings on complex C*-algebras and their fixed points
A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...
متن کامل