- I am a member of the Syracuse University Geometry and Topology research group
- My published papers can also be accessed through Mathscinet. (subscription required)
- You can also follow my articles through my Google Scholar profile.
- The work below has been supported by grants from the National Science Foundation (NSF-DMS CAREER #1654034 and NSF-DMS #0905527) and a grant from the Simons Foundation (#355608, William Wylie).
PhD Students:
- Alice Lim, graduated 2021.
- Erin Griffin, graduated 2021.
- Nicholas Ng, graduated 2023.
- Eric Cochran, current.
- Ralph Xu, current.
- Nazia Valiayakath, current.
Preprints:
- On the geometry of Riemannian manifolds with density, (with D. Yeroshkin) arXiv preprint
- Extended Solitons of the ambient obstruction flow, (with E. Griffin, R. Poddar, and R. Sharma) arXiv preprint
- The soul theorem for manifolds of nonnegative weighted sectional curvature, in preparation.
Publications:
- Rigidity of compact static near-horizon geometries with negative cosmological constant,
Lett. in Math. Phys., 113(29), 2023.
published version (.pdf) Journal Link. - Holonomy restrictions from the curvature operator of the second kind, (with J. Nienhaus, P. Petersen, and M. Wink) Differential Geom. Appl., 88, 2023.
published version (.pdf) Journal Link. arXiv preprint - Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations, (with P. Petersen)
Differential Geom. Appl., 84, 2022.
published version (.pdf) Journal Link. arXiv preprint. - Gradient shrinking Ricci solitons of half harmonic Weyl curvature, (with J.-Y. Wu and P. Wu)
Calc. Var. Partial Differential Equations, 57(5), 2018.
published version (.pdf) Journal Link. arXiv preprint. - New Restrictions on the Topology of Extreme Black Holes, (with M. Khuri and E. Woolgar)
Lett. Math. Phys.,109(3), pp. 661-673, 2019.
published version (.pdf) Journal Link. arXiv preprint. - Curvature-dimension bounds for Lorentzian splitting theorems, (with E. Woolgar)
J. Geom. Phys., 132, pp. 131-145, 2018.
published version (.pdf) Journal Link. arXiv preprint - The weighted connection and sectional curvature for manifolds with density,
(with L. Kennard and D. Yeroshkin) J. Geom. Anal., 29, pp. 957-1001, 2019.
published version (.pdf) Journal Link. arXiv preprint - A warped product version of the Cheeger-Gromoll splitting theorem,
Trans. of AMS, 369(9), pp. 6661-6681, 2017.
published version (.pdf) arXiv preprint Journal Link. - Positive weighted sectional curvature, (with L. Kennard)
Indiana Univ. Math. J., 66(2), pp. 419-462, 2017.
published version (.pdf) arXiv preprint. Journal link. - Cosmological singularity theorems and splitting theorems for N-Bakry-Emery spacetimes,
(with E. Woolgar) J. Math. Physics, 57(2), 2016.
published version (.pdf) arXiv preprint Journal Link. - Some curvature pinching results for manifolds with density,
Proc. Amer. Math. Soc. 144(2), pp. 823-836, 2016.
published version (.pdf) arXiv preprint Journal link. - Sectional curvature for Riemannian manifolds with density, Geometriae Dedicata, 178(1), pp. 151-169, 2015.
published version (.pdf) arXiv preprint. Journal Link - Uniqueness of warped product Einstein metrics and applications, (with C. He & P. Petersen)
J. Geom. Anal., 25(4), pp. 2617-2644, 2015.
published version (.pdf) arXiv preprint. Journal Link - Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons, (with C. He & P. Petersen), J. Reine Angew. Math. (Crelle’s), 2015(707), pp.217-245, 2015.
published version (.pdf) arXiv preprint. Journal link. - Warped Product Rigidity, (with C. He & P. Petersen) Asian J. of Math., 19(1), pp. 135-170, 2015.
published version (.pdf) arXiv prepint. Journal link. - Conformal diffeomorphisms of gradient Ricci solitons and generalized quasi-Einstein manifolds, (with J. Jauregui) J. Geom. Anal., 25(1), pp. 668-708, 2015.
published version (.pdf) arXiv preprint. Journal link. - Warped product Einstein metrics over spaces with constant scalar curvature, (with C. He & P. Petersen) Asian J. Math., 18(1), pp. 159-190, 2014.
published version (.pdf) arXiv preprint. Journal link. - On the classification of warped product Einstein metrics, (with C. He & P. Petersen) Comm. Anal. Geom., 20(2), pp. 271-312, 2012.
published version (.pdf) arXiv preprint. Journal link. - On the classification of gradient Ricci solitons, (with P. Petersen) Geometry & Topology, 14, pp. 2277-2300, 2010.
published version(.pdf) arXiv preprint. Journal link. - Comparison Geometry for the Bakry-Emery Tensor, (with G. Wei) Journal of Differential Geometry, 83(2), pp. 377-406, 2009.
published version(.pdf) arXiv preprint. Journal Link. - Rigidity of gradient Ricci solitons, (with P. Petersen) Pacific Journal of Math. 241(2), pp. 329-345, 2009.
published version(.pdf) arXiv preprint. Journal Link. - On gradient Ricci solitons with symmetry, (with P. Petersen) Proc. Amer. Math. Soc., 137(5):2085-2092, 2009.
published version(.pdf) arXiv preprint. Journal Link. - Complete Shrinking Ricci solitons have finite fundamental group, Proc. Amer. Math. Soc.,136(5):1803-1806, 2008.
published version(.pdf) arXiv preprint. Journal Link. - Comparison Geometry for smooth metric measure spaces, (with G. Wei) Proc. of the 4th ICCM , Hangzhou, China, Vol. II 191-202, 2007. .pdf file
- Noncompact manifolds with non-negative Ricci curvature, J. of Geometric Analysis, 16(3) 535-550, 2006.
published version(.pdf) arXiv preprint. Journal Link.