Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey

Galaz-García, Fernando; Guijarro, Luis; Núñez-Zimbrón, Jesús

doi:10.1017/9781108884136.017

Search citation statements

Order By: Relevance

Paper Sections

Select...

Collapse1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Book1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The exclusion of hyperbolic geometry in Theorem 7.1 is granted by a result of independent interest proved in [30,Remark B], namely, that a closed collapsing Alexandrov 3-space cannot admit hyperbolic geometry. We refer the reader to [30] and the recent survey [31] for additional details.…”

Section: Collapsementioning

confidence: 99%

Three-Dimensional Alexandrov Spaces: A Survey

Galaz-García

Núñez-Zimbrón

2022

Recent Advances in Alexandrov Geometry

View full text Add to dashboard Cite

We survey several results concerning the geometry and topology of threedimensional Alexandrov spaces with the aim of providing a panoramic and up-to-date view of the subject. In particular we present the classification of positively and nonnegatively curved spaces, the geometrization theorem, a discussion of known results for simply-connected and aspherical spaces, the equivariant and topological classifications of closed three-dimensional Alexandrov spaces with isometric compact Lie group actions, and recent developments on collapsing theory.

show abstract

Section: Collapsementioning

confidence: 99%