# Collapsing to Alexandrov spaces with isolated mild singularities

@article{Fujioka2021CollapsingTA,
title={Collapsing to Alexandrov spaces with isolated mild singularities},
journal={Differential Geometry and its Applications},
year={2021}
}
• Published 25 August 2021
• Mathematics
• Differential Geometry and its Applications

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In this paper the comparison result for the heat kernel on Riemannian manifolds with lower Ricci curvature bound by Cheeger and Yau (1981) is extended to locally compact path metric spaces (X,d) with
Let $M$ be an Alexandrov space collapsing to an Alexandrov space $X$ of lower dimension. Suppose $X$ has no proper extremal subsets and let $F$ denote a regular fiber. We slightly improve the result
Let a sequence $M_j$ of Alexandrov spaces collapse to a space $X$ with only weak singularities. T. Yamaguchi constructed a map $f_j:M_j\to X$ for large $j$ called an almost Lipschitz submersion. We
In this paper we are concerned with collapsing phenomena and pinching problems of Riemannian manifolds whose sectional curvatures are uniformly bounded from below. For a positive integer n and for D
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Let X be an n -dimensional Alexandrov space of curvature bounded from below. We define the notion of singular point in X , and prove that the set S χ of singular points in X is of Hausdorff dimension
An $e^\epsilon$-Lipschitz and co-Lipschitz map, as a metric analogue of an $\epsilon$-Riemannian submersion, naturally arises from a sequence of Alexandrov spaces with curvature uniformly bounded
• Mathematics
Communications in Contemporary Mathematics
• 2021
1 We prove the generalized Margulis lemma with a uniform index bound on an Alexandrov [Formula: see text]-space [Formula: see text] with curvature bounded below, i.e. small loops at [Formula: see
T H E O R E M 0. The topological group H(X) of homeomorphisms of a finite simplicial complex X onto itself is locally contractible. This result does not extend to ENR's (euclidean neighborhood