Phone: 316 978-3965
Office: 351 Jabara Hall
Catherine Searle works in Differential Geometry with an emphasis on Comparison Theory. Her research has been focussed on positively and non-negatively curved Riemannian manifolds, which admit "large" isometric group actions, where "large" can be defined in a number of ways. The existence of an isometric group action G on a metric space X leads to information about the space itself and can be used both as a tool to identify the space and as a means to improve the metric on that space. More recently she has been studying isometric group actions in these two contexts, namely, as a tool to identify both Riemannian manifolds and Alexandrov spaces with a lower curvature bound and as a tool to improve the metric on a Riemannian manifold with a G-invariant metric.
Regularization via Cheeger Deformations, with P. Solorzano, F. Wilhelm, Annals of Global Analysis and Geometry, doi:10.1007/s10455-015-9471-3, pp. 1--9 (2015).
How to lift positive Ricci curvature, with F. Wilhelm, Geometry and Topology, 19 (3), pp. 1409-1475 (2015).
Orientation and symmetries of Alexandrov spaces with applications in positive curvature, with J. Harvey, arXiv:math.DG/1209.1366v3 (2012).
An introduction to isometric group actions with applications to spaces with curvature bounded below with applications to spaces with curvature bounded below, Geometry of Manifolds of Non-negative Sectional Curvature, Lecture Notes in Mathematics 2110, DOI 10.1007/978-3-319-06373-7_3, Springer International (2014).
Non-negatively curved 5-manifolds of almost maximal symmetry rank, with F. Galaz-Garcia, Geometry & Topology 18 pp. 1397–1435 (2014).
Cohomogeneity one Alexandrov spaces, with F. Galaz-Garcia, Transformation Groups, Vol. 16, No. 1, pp. 91--107 (2011).
The Hopf Conjecture for Manifolds with Low Cohomogeneity or High Symmetry Rank, with T. Puttmann, Proceedings of the AMS, vol. 130, no. 1, pp. 163--166 (2002).
Differential Topological Restrictions by Curvature and Symmetry, with K. Grove, Journal of Differential Geometry, vol 47, pp. 530--559 (1997), Correction, JDG, vol. 49, p. 205 (1998).
On the Topology of Nonnegatively Curved Simply Connected 4-Manifolds with Continuous Symmetry, with D.G. Yang, Duke Mathematical Journal, vol. 74, no. 2, pp. 547--556 (1994).
Positively Curved Manifolds with Maximal Symmetry Rank, with K. Grove, Journal for Pure and Applied Algebra, vol. 91, pp. 137--142 (1994).
Cohomogeneity One Manifolds of Positive Curvature, Aportaciones Matematicas, serie: Notas de Investigacion no. 8, ISBN 968-36-2793-5, pp. 109--110 (1992).