Publications
On the filling radius of positively curved manifolds. Inventiones Mathematicae,
107 (1992) 653--668.
Collapsing to almost Riemannian spaces. Indiana University Mathematics Journal, 41 (1992) 1119-1142.
On radius, systole, and positive Ricci curvature. Mathematische Zeitschrift, 218 (1995) 597-602.
Hard and soft packing radius theorems, with K. Grove, Annals of Mathematics, 142 (1995) 213-237.
Spaces on and beyond the boundary of existence, with P. Petersen & S. Zhu, Journal of GeometricAnalysis, 5 (1995) 419-426.
The radius rigidity theorem for manifolds of positive curvature. Journal of Differential Geometry, 44 (1996) 634-665.
Metric constraints on exotic spheres via Alexandrov geometry, with K. Grove, Journal für reine und angewandte Mathematik, 487 (1997) 201-217.
On intermediate Ricci curvature and fundamental groups. Illinois Journal of Mathematics, 41 (1997) 488-494.
Exotic spheres with lots of positive curvatures, Journal of Geometric Analysis, 11 (2001) 161-186.
Examples of Riemannian manifolds with positive curvature almost everywhere, with P. Petersen, Geometry and Topology, 3 (1999) 331-367.
An exotic sphere with positive curvature almost everywhere. Journal of Geometric Analysis, 11 (2001) 517-558.
On the diffeomorphism type of certain S3-bundles over S4, with M. Sanchez, Proceedings of the American Mathematical Society, 130 (2001) 1139-1143.
On Frankel's theorem, with P. Petersen, Bulletin of the Canadian Mathematical Society, 46 (2003) 130-139.
Horizontally homothetic submersions and nonnegative curvature, with Y. Ou, Indiana University Mathematics Journal, 56 (2007) 243-262.
An exotic sphere with positive sectional curvature, with P. Petersen, preprint. arXiv:0805.0812 (2008)
Some principles for deforming nonnegative curvature, with P. Petersen, preprint. .arXiv:0908.3026 (2010)
Infinity-harmonic maps and morphisms, with Y. Ou & T. Troutman, Differential Geometry and its Applications, 30 (2012) 164-178.
Flats and submersions in non-negative curvature, with C. Pro, Geometriae Dedicata, 161 (2012) 109-118.
Riemannian submersions need not preserve positive Ricci curvature, with C. Pro, Proceedings of the American Mathematical Society, 142, (2014) 2529–2535.
On Jacobi field splitting theorems, with D. Gumaer, Differential Geometry and its Applications, 37 (2014) 109–119.
How to lift positive Ricci curvature, with C. Searle, Geometry and Topology, 19 (2015) 1409--1475.
The Diffeomorphism type manifolds with almost maximal volume, with C. Pro & M. Sill, Communications in Analysis and Geometry, Vol. 25, No. 1 (2017), pp. 243-267.
The sub-index of critical points of distance functions, with B. Herzog, preprint, arxiv version (no diagrams) arXiv:1409.0132 (2015)
Regularization via Cheeger deformations, with C. Searle and P. Solórzano, Annals of Global Analysis and Geometry, 48, (2015), 295-303.
Crosscap Stability, with C. Pro and M. Sill, Advances in Geometry, 2017; 17 (2):231–245.
Almost nonnegative curvature on some fake RP^6s and RP^14s, with P. Rajan, Bulletin of the Australian Mathematical Society, 94 (2016), 304-315.
Focal radius, rigidity, and lower curvature bounds, with L. Guijarro, Proceedings of the London Mathematical Society, 116 no. 6 (2018) 1519--1552. https://doi.org/10.1112/plms.12113
Diffeomorphism stability and codimension three, with C. Pro, Journal of Geometric Analysis, 31 (2021) 11061–11113 https://doi.org/10.1007/s12220-021-00673-6
Restrictions on submanifolds via focal radius bounds, with L. Guijarro, Mathematical Research Letters, Volume 27, Number 1, 115–139, 2020.
Random manifolds have no totally geodesic submanifolds, with T. Murphy, Michigan Mathematical Journal, 68 (2019), 323–335.
A softer connectivity principle, with L. Guijarro, Communications in Analysis and Geometry, Volume 30, Number 5, 1093–1119, 2022. arXiv:1812.01021 (2020)
On Delaunay Triangulations of Gromov Sets, with C. Pro, preprint. arXiv: 2006.02452 (2020)
Stability, Finiteness and Dimension Four, with C. Pro, preprint. arXiv:2006.02450 (2020)
Random 3-Manifolds Have No Totally Geodesic Submanifolds, with H. El-Hasan, preprint. arXiv:2404.01581 (2024)