Compactifications of Complete Riemannian manifolds and Their Applications
Xiaodong Wang
TL;DR
This paper reviews various methods of compactifying noncompact Riemannian manifolds and surveys recent results, highlighting their importance in understanding the geometric and topological properties of such manifolds.
Contribution
It provides a comprehensive overview of different compactification techniques and recent advances in their applications to Riemannian geometry.
Findings
Multiple compactification methods are compared and analyzed.
Recent results demonstrate new applications in geometric analysis.
Survey highlights open problems and future directions.
Abstract
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Topological and Geometric Data Analysis · Geometry and complex manifolds