منابع مشابه
Properties of Distance Functions on Convex Surfaces and Alexandrov Spaces
If X is a convex surface in a Euclidean space, then the squared (intrinsic) distance function dist(x, y) is d.c. (DC, delta-convex) on X×X in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of dist(x, y) on X × X if X is an Alexandrov space with nonnegative curvature. Applications concerning r-boundaries (distance spheres) and the ambiguous locus (ex...
متن کاملHarmonic Functions on Alexandrov Spaces and Their Applications
The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂M an open domain and f : Ω→ R a harmonic function. Then f is Lipschitz on any compact subset of Ω. Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.
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 کاملFlat graphs based on affine spaces and affine symplectic spaces
Let AG(n,Fq) be the n-dimensional affine space over the finite field Fq. For 0 ≤ m ≤ n − 1, define a graph G whose vertex set is the set of all m-flats of AG(n,Fq), such that two vertices F1 and F2 are adjacent if dim(F1∨F2) = m+1, where F1∨F2 is the minimum flat containing both F1 and F2. Let ASG(2ν,Fq) be the 2ν-dimensional affine-symplectic space over Fq. Define a graph S (ν) whose vertex se...
متن کاملDifferential 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 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: Mathematische Zeitschrift
سال: 2017
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-017-1959-z