English

Existence of Typical Scales for Manifolds with Lower Ricci Curvature Bound

Differential Geometry 2017-03-29 v1

Abstract

For collapsing sequences of Riemannian manifolds which satisfy a uniform lower Ricci curvature bound it is shown that there is a sequence of scales such that for a set of good base points of large measure the pointed rescaled manifolds subconverge to a product of a Euclidean and a compact space. All Euclidean factors have the same dimension, all possible compact factors satisfy the same diameter bounds and their dimension does not depend on the choice of the base point (along a fixed subsequence).

Keywords

Cite

@article{arxiv.1703.09590,
  title  = {Existence of Typical Scales for Manifolds with Lower Ricci Curvature Bound},
  author = {Dorothea Jansen},
  journal= {arXiv preprint arXiv:1703.09590},
  year   = {2017}
}