On Toponogov's comparison theorem for Alexandrov spaces
نویسندگان
چکیده
منابع مشابه
A Splitting Theorem for Alexandrov Spaces
A classical result of Toponogov [12] states that if a complete Riemannian manifold M with nonnegative sectional curvature contains a straight line, thenM is isometric to the metric product of a nonnegatively curved manifold and a line. We then know that the Busemann function associated with the straight line is an affine function, namely, a function which is affine on each unit speed geodesic i...
متن کاملHeat Kernel Comparison on Alexandrov Spaces with Curvature Bounded Below
In this paper the comparison result for the heat kernel on Riemannian manifolds with lower Ricci curvature bound by Cheeger and Yau [CY81] is extended to locally compact path metric spaces (X, d) with lower curvature bound in the sense of Alexandrov and with sufficiently fast asymptotic decay of the volume of small geodesic balls. As corollaries we recover Varadhan’s short time asymptotic formu...
متن کاملA Convergence Theorem in the Geometry of Alexandrov Spaces
The fibration theorems in Riemannian geometry play an important role in the theory of convergence of Riemannian manifolds. In the present paper, we extend them to the Lipschitz submersion theorem for Alexandrov spaces, and discuss some applications. Résumé. Les théorèmes de fibration de la géométrie riemannienne jouent un rôle important dans la théorie de la convergence des variétés riemannienn...
متن کاملGradient Flows on Wasserstein Spaces over Compact Alexandrov Spaces
We establish the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below. By using this Riemannian structure, we formulate and construct gradient flows of functions on such spaces. If the underlying space is a Riemannian manifold of nonnegative sectional curvature, then our gradient flow of the free energy produces a solution of the l...
متن کاملAn almost isometric sphere theorem and weak strainers on Alexandrov spaces
In this paper we define a weak (n+1,ε)−strainer on an Alexandrov space with curvature≥ 1, and prove an almost isometric sphere theorem in the setting of a weak strainer, making use of a rigidity theorem for round spheres. To prove the rigidity theorem we investigate several properties of weak strainers, e.g. the maximality property, the covering property of the balls centered at strainer points...
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: L’Enseignement Mathématique
سال: 2013
ISSN: 0013-8584
DOI: 10.4171/lem/59-3-6