13 citations · 59 across the 34 of their papers we have counts for
30 papers · 1 filter
Point selections from Jordan domains in Riemannian Surfaces
Igor Belegradek, Mohammad Ghomi
Using fiber bundle theory and conformal mappings, we continuously select a point from the interior of Jordan domains in Riemannian surfaces. This selection can be made equivariant…
Hyperbolization and regular neighborhoods
Igor Belegradek
We show that the hyperbolization of polyhedra pulls back regular neighborhoods of PL submanifolds. Applying this to the Riemannian version of the hyperbolization due to Ontaneda gi…
Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics
Igor Belegradek, David González-Álvaro
We give examples of open manifolds that carry infinitely many complete metrics of nonnegative sectional curvature such that they all have the same soul, and their isometry classes…
Index theory and deformations of open nonnegatively curved manifolds
Igor Belegradek
We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivia…
Gromov-Hausdorff hyperspace of nonnegatively curved -spheres
Igor Belegradek
We study topological properties of the Gromov-Hausdorff metric on the set of isometry classes of nonnegatively curved -spheres.
Centers of disks in Riemannian manifolds
Igor Belegradek, Mohammad Ghomi
We prove the existence of a center, or continuous selection of a point, in the relative interior of embedded -disks in Riemannian -manifolds. If the center can…
Smoothness of Minkowski sum and generic rotations
Igor Belegradek, Zixin Jiang
Can the Minkowski sum of two compact convex bodies be made smoother by rotating one of them? We construct two infinitely differentiable strictly convex plane bodies such that after…
Spaces of nonnegatively curved surfaces
Taras Banakh, Igor Belegradek
We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on surfaces of positive Euler characteristic equipped with the topology of un…
Space of nonnegatively curved metrics and pseudoisotopies
Igor Belegradek, F. Thomas Farrell, Vitali Kapovitch
Let V be an open manifold with complete nonnegatively curved metric such that the normal sphere bundle to a soul has no section. We prove that the souls of nearby nonnegatively cur…
Connectedness properties of the space of complete nonnegatively curved planes
Igor Belegradek, Jing Hu
We study the space of complete Riemannian metrics of nonnegative curvature on the plane equipped with the C^k topology. If k is infinite, we show that the space is homeomorphic to…
Topology of open nonpositively curved manifolds
Igor Belegradek
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fun…
An assortment of negatively curved ends
Igor Belegradek
Motivated by a recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with the real line admits…
Non-aspherical ends and nonpositive curvature
Igor Belegradek, T. Tam Nguyen Phan
We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonposi…
Rays and souls in von Mangoldt planes
Igor Belegradek, Eric Choi, Nobuhiro Innami
We study rays in von Mangoldt planes, which has applications to the structure of open complete manifolds with lower radial curvature bounds. We prove that the set of souls of any r…
Codimension two souls and cancellation phenomena
Igor Belegradek, Slawomir Kwasik, Reinhard Schultz
For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomo…
Moduli spaces of nonnegative sectional curvature and non-unique souls
Igor Belegradek, Slawomir Kwasik, Reinhard Schultz
We apply various topological methods to distinguish connected components of moduli spaces of complete Riemannian metrics of nonnegative sectional curvature on open manifolds. The n…
Degenerations of Riemannian manifolds
Igor Belegradek
This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometri…
Pinching estimates for negatively curved manifolds with nilpotent fundamental groups
Igor Belegradek, Vitali Kapovitch
Let be a complete Riemannian metric of sectional curvature within whose fundamental group contains a -step nilpotent subgroup of finite index. We prove that $a\g…
Classification of negatively pinched manifolds with amenable fundamental groups
Igor Belegradek, Vitali Kapovitch
We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the Möbius band, and the products of a l…
Nonnegative curvature, symmetry and fundamental group
Igor Belegradek
We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two ``splitting in a finite cover'' theorems for isometric group actions on Riemannian…
Pinching surface groups in complex hyperbolic plane
Igor Belegradek
We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.
Vector bundles with infinitely many souls
Igor Belegradek
We construct the first examples of manifolds, the simplest one being the product of S^3, S^4, and R^5, which admit infinitely many complete nonnegatively curved metrics with pairwi…
Metrics of positive Ricci curvature on bundles
Igor Belegradek, Guofang Wei
We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particu…
Metrics of positive Ricci curvature on vector bundles over nilmanifolds
Igor Belegradek, Guofang Wei
We construct metrics of positive Ricci curvature on some vector bundles over tori (or more generally, over nilmanifolds). This gives rise to the first examples of manifolds with po…