Lipschitz Homotopy Convergence of Alexandrov Spaces

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A 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 کامل

Differential Geometric Aspects of Alexandrov Spaces

We summarize the results on the differential geometric structure of Alexandrov spaces developed in [Otsu and Shioya 1994; Otsu 1995; Otsu and Tanoue a]. We discuss Riemannian and second differentiable structure and Jacobi fields on Alexandrov spaces of curvature bounded below or above.

متن کامل

Quasigeodesics and Gradient Curves in Alexandrov Spaces

1. A comparison theorem for complete Riemannian manifolds with sectional curvatures ≥ k says that distance functions in such manifolds are more concave than in the model space Sk of constant curvature k. In other words, the restriction of any distance function distp to any geodesic γ (always parametrised by the arclength) satisfies a certain concavity condition (∗)k. For example, the condition ...

متن کامل

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 کامل

Topological regularity theorems for Alexandrov spaces

Since Gromov gave in [G1], [G2] an abstract definition of Hausdorff distance between two compact metric spaces, the Gromov-Hausdorff convergence theory has played an important role in Riemannian geometry. Usually, Gromov-Hausdorff limits of Riemannian manifolds are almost never Riemannian manifolds. This motivates the study of Alexandrov spaces which are more singular than Riemannian manifolds ...

متن کامل

ذخیره 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: The Journal of Geometric Analysis

سال: 2018

ISSN: 1050-6926,1559-002X

DOI: 10.1007/s12220-018-0075-6