Degenerations of Riemannian manifolds

Details Degenerations of Riemannian manifolds Degenerations of Riemannian manifolds

2007-01-25

arxiv.org/abs/math/0701723v2

Mathematics

Differential Geometry

references added, 11 pages

Scientific paper

This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological structure of collapsed/non-collapsed regions in Riemannian manifold under various curvature assumptions. Numerous applications of collapsing theory to Riemannian geometry are NOT discussed in this survey.

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