27 citations · 68 across the 17 of their papers we have counts for
21 papers · 1 filter
Kähler-Ricci solitons with almost maximal symmetry
Ha Tuan Dung, Catherine Searle, Hung Tran
This paper studies a non-trivial gradient Kähler-Ricci soliton, of complex dimension , with an isometry group of dimension at least . We show that the isometry group acts…
Symmetries of Spaces with Lower Curvature Bounds
Catherine Searle
This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.
Positive -intermediate scalar curvature and cobordism
Matthew Burkemper, Catherine Searle, Mark Walsh
In this paper we consider a well-known construction due to Gromov and Lawson, Schoen and Yau, Gajer, and Walsh which allows for the extension of a metric of positive scalar curvatu…
Positive curvature and discrete abelian symmetry
Lee Kennard, Elahe Khalili Samani, Catherine Searle
By replacing the torus with an elementary abelian two-group, we generalize the maximal symmetry result of Grove and Searle and the half-maximal symmetry result of Wilking for posit…
Odd-dimensional GKM-manifolds of non-negative curvature
Christine Escher, Oliver Goertsches, Catherine Searle
We prove for closed, odd-dimensional GKM manifolds of non-negative sectional curvature that both the equivariant and the ordinary rational cohomology split off the cohomology o…
Almost non-negatively curved 4-manifolds with torus symmetry
John Harvey, Catherine Searle
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also ad…
Almost Isotropy-Maximal Manifolds of Non-negative Curvature
Zheting Dong, Christine Escher, Catherine Searle
We extend the equivariant classification results of Escher and Searle for closed, simply connected, non-negatively curved Riemannian -manifolds admitting isometric isotropy-maxi…
Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry in dimension 4
John Harvey, Catherine Searle
We classify positively curved Alexandrov spaces of dimension 4 with an isometric circle action up to equivariant homeomorphism, subject to a certain additional condition on the inf…
Alexandrov Spaces with Integral Current Structure
Maree Jaramillo, Raquel Perales, Priyanka Rajan +2
We endow each closed, orientable Alexandrov space with an integral current of weight equal to 1, , in other words, we prove that $(X, d…
Non-negatively curved 6-manifolds with almost maximal symmetry rank
Christine Escher, Catherine Searle
We classify closed, simply-connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism.
Non-negative curvature and torus actions
Christine Escher, Catherine Searle
Let be the class of closed, simply-connected, non-negatively curved Riemannian manifolds admitting an isometric, effective, isotropy-maximal torus action. We pr…
Regularization via Cheeger Deformations
Catherine Searle, Pedro Solórzano, Frederick Wilhelm
We show that Cheeger deformations regularize --invariant metrics in a very strong sense.
How to lift positive Ricci curvature
Catherine Searle, Frederick Wilhelm
We show how to lift positive Ricci and almost non-negative curvatures from an orbit space to the corresponding -manifold, . We apply the results to get new examples of…
Orientation and symmetries of Alexandrov spaces with applications in positive curvature
John Harvey, Catherine Searle
We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact…
Positively curved manifolds with maximal symmetry rank
Karsten Grove, Catherine Searle
The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric wi…
Low-dimensional manifolds with non-negative curvature and maximal symmetry rank
Fernando Galaz-Garcia, Catherine Searle
We classify closed, simply connected -manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions . I…
Global G-Manifold reductions and resolutions
Karsten Grove, Catherine Searle
The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.
The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank
Thomas Puettmann, Catherine Searle
We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold…
Non-negatively curved 5-manifolds with almost maximal symmetry rank
Fernando Galaz-Garcia, Catherine Searle
We show that a closed, simply-connected, non-negatively curved 5-manifold admitting an effective, isometric action is diffeomorphic to one of , , $S^3\til…
Cohomogeneity One Alexandrov Spaces
Fernando Galaz-Garcia, Catherine Searle
We obtain a structure theorem for closed, cohomogeneity one Alexandrov spaces and we classify closed, cohomogeneity one Alexandrov spaces in dimensions 3 and 4. As a corollary, we…
Non-negatively Curved Manifolds with Maximal Symmetry Rank in Low Dimensions
Fernando Galaz-Garcia, Catherine Searle
We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric or action. As a direct consequence, we show that for a…