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Compactifications of Complete Riemannian manifolds and Their Applications
Compactifications Complete Riemannian manifolds Applications
2011/1/21
To study a noncompact Riemannian manifold, it is often useful to find a compactification
or attach a boundary. For example, in hyperbolic geometry a lot of investigation is carried out on the sphere ...
Liouville-type theorems and applications to geometry on complete Riemannian manifolds
Liouville-type theorems geometry complete Riemannian manifolds
2010/11/11
On a complete Riemannian manifold M with Ricci curvature satisfying $$\textrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2...(\log^{k}r)^2$$ for $r\gg 1$, where A>0 is a constant, and ...
The Infinity of Complete Riemannian Manifolds under Yamabe Flow
Yamabe flow locally conformally flat asymptotic volume ratio
2018/4/19
We study complete locally conformally flat Riemannian manifolds Mn.We prove that the flatness of the infinity geometry can be preserved under the Yamabe flow. As an immediate application, the asymptot...