## References

SHOWING 1-10 OF 16 REFERENCES

### Heat Kernel Comparison on Alexandrov Spaces with Curvature Bounded Below

- Mathematics
- 2004

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…

### Application of good coverings to collapsing Alexandrov spaces

- MathematicsPacific Journal of Mathematics
- 2022

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…

### A fibration theorem for collapsing sequences of Alexandrov spaces

- Mathematics
- 2019

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…

### Collapsing and pinching under a lower curvature bound

- Mathematics
- 1991

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…

### The Riemannian structure of Alexandrov spaces

- Mathematics
- 1994

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…

### Homotopy lifting property of an $e^ε$-Lipschitz and co-Lipschitz map

- Mathematics
- 2012

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…

### Margulis lemma and Hurewicz fibration theorem on Alexandrov spaces

- MathematicsCommunications 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…

### Deformation of homeomorphisms on stratified sets

- Mathematics
- 1972

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…