LOCALLY PERIPHERALLY EUCLIDEAN SPACES ARE LOCALLY EUCLIDEAN, II

Locally Peripherally Euclidean Spaces Are Locally Euclidean, Ii.

A Characterization of Locally Euclidean Spaces

Ricci Flatness of Asymptotically Locally Euclidean Metrics

In this article we study the metric property and the function theory of asymptotically locally Euclidean (ALE) Kähler manifolds. In particular, we prove the Ricci flatness under the assumption that the Ricci curvature of such manifolds is either nonnegative or nonpositive. The result provides a generalization of previous gap type theorems established by Greene and Wu, Mok, Siu and Yau, etc. It ...

On the Locally Branched Euclidean Metric Gauge

A metric gauge on a set is a maximal collection of metrics on the set such that the identity map between any two metrics from the collection is locally bi-Lipschitz. We characterize metric gauges that are locally branched Euclidean and discuss an obstruction to removing the branching. Our characterization is a mixture of analysis, geometry, and topology with an argument of Yu. Reshetnyak to pro...

A Theorem on Locally Euclidean Groups

1. Let G be a connected locally compact group and let G' denote the closure of the commutator subgroup of G. G' is called the derived subgroup of G. Consider the derived series of G, that is, the sequence of subgroups Go, Gi, ■ ■ ■ , Gn, ■ ■ ■ where G0 = G and Gn+i = G'nEach Gn is connected and this sequence becomes stationary at some finite stage,2 that is, for some n, Gn = Gn+i. We define Gn ...