Add to ORKGWe investigate manifolds with small excess, curvature bounded from below, and diameter bounded from above. In particular, we prove the Double Soul conjecture of K. Grove and P. Petersen in dimension 3. In order to prove this we give some new ideas and results on collapsing of Riemannian manifolds. A. D. Alexandrov\u27s spaces enter here as limit spaces, in the (pointed) Gromov-Hausdorff topology, of collapsing sequences of Riemannian manifolds whose curvatures are uniformly bounded from below
We generalize the Alexandrov-Toponogov comparison theorem to the case of complete Riemannian manifol...
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a l...
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a l...
Abstract. In this paper, we study the topology of topologically regular 4-dimensional open non-negat...
81 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.The second main result identif...
81 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.The second main result identif...
We survey works on collapsing Riemannian manifolds with a lower bound of sectional curvature, focusi...
In this work, we describe a method to construct new examples of collapse with a lower curvature boun...
Abstract. Suppose that a sequence of Riemannian manifolds with Ricci curvature ≥ −k2 converges to a ...
In [7], Gromov introduced a notion, Hausdorff distance, between two metric spaces. Several authors f...
This thesis has two primary parts. In the first part we study shrinking Ricci solitons. We classify ...
We prove that the Euler characteristic of a collapsing Alexandrov space is equal to the sum of the p...
AbstractWhen phrased in terms of Hausdorff convergence, M. Gromov's almost flat manifold theorem sta...
The purpose of this paper is to completely characterize the topology of three-dimensional Riemannian...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
We generalize the Alexandrov-Toponogov comparison theorem to the case of complete Riemannian manifol...
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a l...
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a l...
Abstract. In this paper, we study the topology of topologically regular 4-dimensional open non-negat...
81 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.The second main result identif...
81 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.The second main result identif...
We survey works on collapsing Riemannian manifolds with a lower bound of sectional curvature, focusi...
In this work, we describe a method to construct new examples of collapse with a lower curvature boun...
Abstract. Suppose that a sequence of Riemannian manifolds with Ricci curvature ≥ −k2 converges to a ...
In [7], Gromov introduced a notion, Hausdorff distance, between two metric spaces. Several authors f...
This thesis has two primary parts. In the first part we study shrinking Ricci solitons. We classify ...
We prove that the Euler characteristic of a collapsing Alexandrov space is equal to the sum of the p...
AbstractWhen phrased in terms of Hausdorff convergence, M. Gromov's almost flat manifold theorem sta...
The purpose of this paper is to completely characterize the topology of three-dimensional Riemannian...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
We generalize the Alexandrov-Toponogov comparison theorem to the case of complete Riemannian manifol...
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a l...
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a l...