William Wylie

I am generally interested in mathematical problems that relate and combine analysis, geometry, and topology and my research focus is in the fields of Riemannian geometry and geometric analysis.

My recent research projects have focused on aspects of the theory of Ricci curvature for metric measure spaces. One direction in this work is comparison geometry for the Bakry-Emery Ricci curvature, which was introduced in the probability setting and has fundamental connections to the theory of optimal transport. The second is gradient Ricci solitons, which appear naturally as "canonical" metrics from the perspective of manifolds with measure and are intimately related to the study of the Ricci flow. The third is the study of warped product Einstein metrics, which is an old problem in Riemannian geometry and general relativity which the theory of manifolds with measure casts in a new light.

Below are links to my preprints and publications. For the list of publications complete with abstracts, click here.

1. (with C. He & P. Petersen) On the classification of warped product Einstein metrics. arXiv.
2. (with C. He & P. Petersen) Warped product Einstein metrics over spaces with constant scalar curvature. arXiv.
3. (with C. He & P. Petersen) The space of virtual solutions to the warped product Einstein equation. In preparation.

7. (with P. Petersen) On the classification of gradient Ricci solitons. Geometry & Topology, 14, pp. 2277-2300, 2010. available online.
6. (with G. Wei) Comparison Geometry for the Bakry-Emery Tensor. Journal of Differential Geometry, 83(2), pp. 377-406, 2009. available online.
5. (with P. Petersen) Rigidity of gradient Ricci solitons. Pacific Journal of Math., 241(2), pp. 329-345, 2009. available online.
4. (with P. Petersen) On gradient Ricci solitons with symmetry. Proc. Amer. Math. Soc.,137(5):2085-2092, 2009. available online.
3. Shrinking Ricci solitons have finite fundamental group. Proc. Amer. Math. Soc.,136(5):1803-1806, 2008. available online.
2. (with G. Wei) Comparison Geometry for smooth metric measure spaces. Proc. of the 4th ICCM , Hangzhou, China, Vol. II 191-202, 2007. pdf file.
1. Noncompact manifolds with non-negative Ricci curvature. J. of Geometric Analysis, 16(3) 535-550, 2006. available online.