PhD Students:


  1. On the geometry of Riemannian manifolds with density, (with D. Yeroshkin) arXiv preprint


  1. Rigidity of compact static near-horizon geometries with negative cosmological constant, 
    Lett. in Math. Phys., 113(29), 2023.
    Journal Link.
  2. Holonomy restrictions from the curvature operator of the second kind, (with J. Nienhaus, P. Petersen, and M. Wink) Differential Geom. Appl., 88, 2023.
    Journal Link. arXiv preprint
  3. Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations, (with P. Petersen)
    Differential Geom. Appl., 84, 2022.
    Journal Link. arXiv preprint.
  4. Gradient shrinking Ricci solitons of half harmonic Weyl curvature, (with J.-Y. Wu and P. Wu)
    Calc. Var. Partial Differential Equations, 57(5), 2018.
    Journal Link. arXiv preprint.
  5. New Restrictions on the Topology of Extreme Black Holes, (with M. Khuri and E. Woolgar)
    Lett. Math. Phys.,109(3), 661-673, 2019.
    Journal Link. arXiv preprint.
  6. Curvature-dimension bounds for Lorentzian splitting theorems, (with E. Woolgar)
    J. Geom. Phys., 132, pp. 131-145, 2018.
    Journal Link. arXiv preprint
  7. The weighted connection and sectional curvature for manifolds with density,
    (with L. Kennard and D. Yeroshkin) J. Geom. Anal., 2018.
    Journal Link. arXiv preprint
  8. A warped product version of the Cheeger-Gromoll splitting theorem,
    Trans. of AMS, 369(9), pp. 6661-6681, 2017.
    arXiv preprint Journal Link.
  9. Positive weighted sectional curvature, (with L. Kennard)
    Indiana Univ. Math. J.,  66(2), pp. 419-462, 2017.
    published version (.pdf) arXiv preprint. Journal link.
  10. 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.
  11. 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.
  12. Sectional curvature for Riemannian manifolds with density, Geometriae Dedicata, 178(1), pp. 151-169, 2015.
    published version (.pdf) arXiv preprint. Journal Link
  13. 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
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. On the classification of gradient Ricci solitons, (with P. Petersen)  Geometry & Topology, 14, pp. 2277-2300, 2010.
    published version(.pdf) arXiv preprint. Journal link.
  20. 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.
  21. 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.
  22. 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.
  23. Complete Shrinking Ricci solitons have finite fundamental group, Proc. Amer. Math. Soc.,136(5):1803-1806, 2008.
    published version(.pdf)  arXiv preprint. Journal Link.
  24. Comparison Geometry for smooth metric measure spaces, (with G. Wei)  Proc. of the 4th ICCM , Hangzhou, China, Vol. II 191-202, 2007. pdf file.
  25. Noncompact manifolds with non-negative Ricci curvature, J. of Geometric Analysis, 16(3) 535-550, 2006.
    published version(.pdf) arXiv preprint. Journal Link.