Geometry & Topology Volume 18, issue 2 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Procedure

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Other MSP Journals

Sweeping out sectional curvature

Dmitri Panov and Anton Petrunin

Geometry & Topology 18 (2014) 617–631

DOI: 10.2140/gt.2014.18.617

Bibliography

1	A D Aleksandrov, Vnutrennyaya Geometriya Vypuklyh Poverhnosteĭ, OGIZ, Moscow-Leningrad, (1948) 387 MR0029518
2	S B Alexander, I D Berg, R L Bishop, Geometric curvature bounds in Riemannian manifolds with boundary, Trans. Amer. Math. Soc. 339 (1993) 703 MR1113693
3	S B Alexander, V Kapovitch, A Petrunin, Alexandrov geometry
4	S Brendle, F C Marques, A Neves, Deformations of the hemisphere that increase scalar curvature, Invent. Math. 185 (2011) 175 MR2810799
5	S V Buyalo, Volume and fundamental group of a manifold of nonpositive curvature, Mat. Sb. 122(164) (1983) 142 MR717671
6	J Cheeger, D G Ebin, Comparison theorems in Riemannian geometry, AMS Chelsea Publishing (2008) MR2394158
7	M Gromov, Sign and geometric meaning of curvature, Rend. Sem. Mat. Fis. Milano 61 (1991) 9 MR1297501
8	F Hang, X Wang, Rigidity theorems for compact manifolds with boundary and positive Ricci curvature, J. Geom. Anal. 19 (2009) 628 MR2496569
9	J Lohkamp, Global and local curvatures, from: "Riemannian geometry" (editors M Lovrić, M Min-Oo, M Y K Wang), Fields Inst. Monogr. 4, Amer. Math. Soc. (1996) 23 MR1377308
10	J Lott, On the long-time behavior of type-III Ricci flow solutions, Math. Ann. 339 (2007) 627 MR2336062
11	M Min-Oo, Scalar curvature rigidity of asymptotically hyperbolic spin manifolds, Math. Ann. 285 (1989) 527 MR1027758
12	M Min-Oo, Scalar curvature rigidity of certain symmetric spaces, from: "Geometry, topology, and dynamics" (editor F Lalonde), CRM Proc. Lecture Notes 15, Amer. Math. Soc. (1998) 127 MR1619128
13	A Petrunin, W Tuschmann, Diffeomorphism finiteness, positive pinching, and second homotopy, Geom. Funct. Anal. 9 (1999) 736 MR1719602
14	R Schoen, S T Yau, Proof of the positive mass theorem, II, Comm. Math. Phys. 79 (1981) 231 MR612249
15	E Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981) 381 MR626707
16	V A Zalgaller, On deformations of a polygon on a sphere, Uspehi Mat. Nauk 11 (1956) 177 MR0083768
17	W Ziller, Examples of Riemannian manifolds with non-negative sectional curvature, from: "Surveys in differential geometry, Vol. XI" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, International Press (2007) 63 MR2408264