Biharmonic Maps on Principal $G$ -Bundles over Complete Riemannian Manifolds of Nonpositive Ricci Curvature

2019 ◽  
Vol 68 (1) ◽  
pp. 19-31
Author(s):  
Hajime Urakawa
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Biharmonic Maps ◽  
Complete Riemannian Manifolds

scholarly journals On low-dimensional Ricci limit spaces

2013 ◽  
Vol 209 ◽  
pp. 1-22 ◽  
Author(s):  
Shouhei Honda
Keyword(s):  
Lower Bound ◽  
Hausdorff Dimension ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Limit Space ◽  
Low Dimensional ◽  
Complete Riemannian Manifolds

AbstractWe call a Gromov–Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. Furthermore, we prove that any Ricci limit space has integral Hausdorff dimension, provided that its Hausdorff dimension is not greater than 2. We also classify 1-dimensional Ricci limit spaces.

scholarly journals Sharp gradient estimates for eigenfunctions on Riemannian manifolds

1998 ◽  
Vol 57 (2) ◽  
pp. 253-259 ◽  
Author(s):  
Albert Borbély
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Gradient Estimates ◽  
Bounded Below ◽  
Complete Riemannian Manifolds

Sharp gradient estimates are derived for positive eigenfunctions on complete Riemannian manifolds with Ricci curvature bounded below.

scholarly journals A Schwarz lemma for complete Riemannian manifolds

1997 ◽  
Vol 55 (3) ◽  
pp. 513-515
Author(s):  
Leung-Fu Cheung ◽  
Pui-Fai Leung
Keyword(s):  
Ricci Curvature ◽  
Distance Function ◽  
Riemannian Manifolds ◽  
Conformal Mappings ◽  
Schwarz Lemma ◽  
Partial Result ◽  
Bounded Below ◽  
Complete Riemannian Manifolds

We prove a Schwarz Lemma for conformal mappings between two complete Riemannian manifolds when the domain manifold has Ricci curvature bounded below in terms of its distance function. This gives a partial result to a conjecture of Chua.

Sign in / Sign up

Export Citation Format

Share Document