• 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).


  1. Curvature-dimension bounds for Lorentzian splitting theorems, (with E. Woolgar) arXiv preprint
  2. The weighted connection and sectional curvature for manifolds with density, (with L. Kennard and D. Yeroshkin) arXiv preprint
  3. On the geometry of Riemannian manifolds with density, (with D. Yeroshkin) arXiv preprint
  4. Gradient shrinking Ricci solitons of half harmonic Weyl curvature, (with J.-Y. Wu and P. Wu) arXiv preprint


  1. A warped product version of the Cheeger-Gromoll splitting theorem,
    Trans. of AMS, 369(9), pp. 6661-6681, 2017.
    arXiv preprint Journal Link.
  2. Positive weighted sectional curvature, (with L. Kennard)
    Indiana Univ. Math. J.,  66(2), pp. 419-462, 2017.
    published version (.pdf) arXiv preprint. Journal link.
  3. 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.
  4. 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.
  5. Sectional curvature for Riemannian manifolds with density, Geometriae Dedicata, 178(1), pp. 151-169, 2015.
    published version (.pdf) arXiv preprint. Journal Link
  6. 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
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. On the classification of gradient Ricci solitons, (with P. Petersen)  Geometry & Topology, 14, pp. 2277-2300, 2010.
    published version(.pdf) arXiv preprint. Journal link.
  13. 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.
  14. 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.
  15. 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.
  16. Complete Shrinking Ricci solitons have finite fundamental group, Proc. Amer. Math. Soc.,136(5):1803-1806, 2008.
    published version(.pdf)  arXiv preprint. Journal Link.
  17. Comparison Geometry for smooth metric measure spaces, (with G. Wei)  Proc. of the 4th ICCM , Hangzhou, China, Vol. II 191-202, 2007. pdf file.
  18. Noncompact manifolds with non-negative Ricci curvature, J. of Geometric Analysis, 16(3) 535-550, 2006.
    published version(.pdf) arXiv preprint. Journal Link.