Manifolds with almost equal diameter and injectivity radius
نویسندگان
چکیده
منابع مشابه
Injectivity Radius of Lorentzian Manifolds
Motivated by the application to spacetimes of general relativity we investigate the geometry and regularity of Lorentzianmanifolds under certain curvature and volume bounds. We establish several injectivity radius estimates at a point or on the past null cone of a point. Our estimates are entirely local and geometric, and are formulated via a reference Riemannian metric that we canonically asso...
متن کاملInjectivity Radius and Fundamental Groups of Hyperbolic 3-manifolds
It is shown that for each integer n > 1 there exists a constant Rn > 0 such that if M is a closed hyperbolic 3-manifold with Rank π1(M) = n, then the injectivity radius of M is bounded above by Rn.
متن کاملCurvature and Injectivity Radius Estimates for Einstein 4-manifolds
It is of fundamental interest to study the geometric and analytic properties of compact Einstein manifolds and their moduli. In dimension 2 these problems are well understood. A 2-dimensional Einstein manifold, (M, g), has constant curvature, which after normalization, can be taken to be −1, 0 or 1. Thus, (M, g) is the quotient of a space form and the metric, g, is completely determined by the ...
متن کاملInjectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of ...
متن کاملGraphs with specified radius and diameter
The radius and diameter of a graph are known to satisfy the relation rad G < diam C 5 2 rad G. We show that this is the only restriction on these parameters and construl*t all nonisomorphic graphs of minimal order having a specified radius and diameter. In a graph G the diameter is diam G = ma,\_inax, d(tc, u) and the radius is rad G = min, max, d(tl, u), the min and max being taken over all po...
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: Journal of Differential Geometry
سال: 1984
ISSN: 0022-040X
DOI: 10.4310/jdg/1214438687