Volume growth of open manifolds with nonnegative curvature

1990 ◽  
Vol 8 (2) ◽  
pp. 159-165
Author(s):  
Viktor Schroeder ◽  
Martin Strake
Keyword(s):  
Volume Growth ◽  
Nonnegative Curvature ◽  
Open Manifolds

Complete open manifolds of nonnegative curvature

1974 ◽  
Vol 15 (1) ◽  
pp. 126-136 ◽  
Author(s):  
V. A. Sharafutdinov
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

Open manifolds of nonnegative curvature

1991 ◽  
Vol 55 (6) ◽  
pp. 2115-2130
Author(s):  
V. B. Marenich ◽  
V. A. Toponogov
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

scholarly journals Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature

2015 ◽  
Vol 2015 (700) ◽  
pp. 1-36 ◽  
Author(s):  
Bobo Hua ◽  
Jürgen Jost ◽  
Shiping Liu
Keyword(s):  
Riemannian Manifolds ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Geometric Analysis ◽  
Nonnegative Curvature ◽  
Doubling Property ◽  
Alexandrov Geometry ◽  
Combinatorial Curvature ◽  
Volume Doubling

AbstractWe apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature. We obtain the metric classification of these graphs and construct the graphs embedded in the projective plane minus one point. Moreover, we show the volume doubling property and the Poincaré inequality on such graphs. The quadratic volume growth of these graphs implies the parabolicity. Finally, we prove the polynomial growth harmonic function theorem analogous to the case of Riemannian manifolds.

scholarly journals The holonomy in open manifolds of nonnegative curvature.

1996 ◽  
Vol 43 (2) ◽  
pp. 263-272 ◽  
Author(s):  
Valery Marenich
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds
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