32 citations · 112 across the 15 of their papers we have counts for
17 papers
Alexandrov Spaces with Maximal Radius
Karsten Grove, Peter Petersen
Abstract. In this paper we prove several rigidity theorems related to and including Lytchak's problem. The focus is on Alexandrov spaces with \curv\geq1, nonempty boundary, and max…
The Boundary Conjecture for Leaf Spaces
Karsten Grove, Adam Moreno, Peter Petersen
We prove that the boundary of an orbit space or more generally a leaf space of a singular Riemannian foliation is an Alexandrov space in its intrinsic metric, and that its lower cu…
Rank three geometry and positive curvature
Fuquan Fang, Karsten Grove, Gudlaugur Thorbergsson
An axiomatic characterization of buildings of type $\CC_3$ due to Tits is used to prove that any cohomogeneity two polar action of type $\CC_3$ on a positively curved simply connec…
Rigidity theorems for submetries in positive curvature
Xiaoyang Chen, Karsten Grove
We derive general structure and rigidity theorems for submetries , where is a Riemannian manifold with sectional curvature . When applied to a non-tri…
Reflection groups in non-negative curvature
Fuquan Fang, Karsten Grove
We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, a…
A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry
Karsten Grove, Burkhard Wilking
We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular se…