scholarly journals Equivariant Alexandrov Geometry and Orbifold Finiteness

2015 ◽  
Vol 26 (3) ◽  
pp. 1925-1945 ◽  
Author(s):  
John Harvey
Keyword(s):  
Alexandrov Geometry

scholarly journals A new proof of almost isometry theorem in Alexandrov geometry with curvature bounded below

2013 ◽  
Vol 17 (4) ◽  
pp. 715-728
Author(s):  
Xiaole Su ◽  
Hongwei Sun ◽  
Yusheng Wang
Keyword(s):  
Alexandrov Geometry ◽  
Bounded Below

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 An Invitation to Alexandrov Geometry

2019 ◽  
Author(s):  
Stephanie Alexander ◽  
Vitali Kapovitch ◽  
Anton Petrunin
Keyword(s):  
Alexandrov Geometry

scholarly journals Extrinsic curvature of semiconvex subspaces in Alexandrov geometry

2009 ◽  
Vol 37 (3) ◽  
pp. 241-262 ◽  
Author(s):  
Stephanie B. Alexander ◽  
Richard L. Bishop
Keyword(s):  
Extrinsic Curvature ◽  
Alexandrov Geometry

scholarly journals Globalization with probabilistic convexity

2015 ◽  
Vol 07 (04) ◽  
pp. 719-735 ◽  
Author(s):  
Nan Li
Keyword(s):  
Basic Tool ◽  
Alexandrov Geometry

We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.

scholarly journals A finite quotient of join in Alexandrov geometry

2020 ◽  
Vol 374 (2) ◽  
pp. 1095-1124 ◽  
Author(s):  
Xiaochun Rong ◽  
Yusheng Wang
Keyword(s):  
Alexandrov Geometry ◽  
Finite Quotient
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