Frontiers of Mathematics in China >
Radius of locally convex subsets in Alexandrov spaces with curvature≥1 and radius>π/2
Received date: 15 Aug 2013
Accepted date: 27 Oct 2013
Published date: 01 Apr 2014
Copyright
Let X be a complete Alexandrov space with curvature≥1 and radius>π/2. We prove that any connected, complete, and locally convex subset without boundary in X also has the radius>π/2.
Key words： Alexandrov space; convex subset; radius
Yusheng WANG , Zhongyang SUN . Radius of locally convex subsets in Alexandrov spaces with curvature≥1 and radius>π/2[J]. Frontiers of Mathematics in China, 2014 , 9(2) : 417 -423 . DOI: 10.1007/s11464-013-0341-7
| 1 |
BuragoY, GromovM, Perel’manA D. Alexandrov spaces with curvature bounded below. Uspekhi Mat Nauk, 1992, 47: 3-51
|
| 2 |
CheegerJ, EbinD G. Comparison Theorems in Riemannian Geometry. Amsterdam: North-Holland Publishing Company, 1975
|
| 3 |
GroveK, PetersenP. A radius sphere theorem. Invent Math, 1993, 112: 577-583
|
| 4 |
GroveK, ShiohamaK. A generalized sphere theorem. Ann Math, 1977, 106: 201-211
|
| 5 |
Perel’manG. Alexandrov’s spaces with curvature bounded from below II. Preprint
|
| 6 |
Perel’manG, PetruninA. Quasigeodesics and gradient curves in Alexandrov spaces. 1994, Preprint
|
| 7 |
WangQ. On the geometry of positively curved manifolds with large radius. Illinois J Math, 2004, 48(1): 89-96
|
| 8 |
XiaC. Some applications of critical point theory of distance functions on Riemannian manifolds. Compos Math, 2002, 132: 49-55
|
| 9 |
YamaguchiT. Collapsing 4-manifolds under a lower curvature bound. 2002, Preprint
|
/
| 〈 |
|
〉 |