Jeffrey S. Case
Assistant Professor
The Pennsylvania State University, Department of Mathematics

Contents: Publications
  1. Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor, J. Geom. Phys. 60(3):477--490, 2010.
    Journal link. arXiv preprint.
  2. On the nonexistence of quasi-Einstein metrics, Pacific J. Math. 248(2):277--284, 2010.
    Journal link. arXiv preprint.
  3. (with Yujen Shu and Guofang Wei) Rigidity of quasi-Einstein metrics, Diff. Geo. Appl., 29(1):93--100, 2011.
    Journal link. arXiv preprint.
  4. Smooth metric measure spaces, quasi-Einstein metrics, and tractors, Cent. Eur. J. Math., 10(5):1733--1762, 2012.
    Journal link. arXiv preprint.
  5. Smooth metric measure spaces and quasi-Einstein metrics, Internat. J. Math., 23(10):1250110, 36 pp., 2012.
    Journal link. arXiv preprint.
  6. Sharp metric obstructions for quasi-Einstein metrics, J. Geom. Phys., 64(2):12--30, 2013.
    Journal link. arXiv preprint.
  7. Conformal invariants measuring the best constants for Gagliardo-Nirenberg-Sobolev inequalities, Calc. Var. PDE, 48(3-4):507--526, 2013.
    Journal link. arXiv preprint.
  8. (with Paul Yang) A Paneitz-type operator for CR pluriharmonic functions, Bull. Inst. Math. Acad. Sin. (N.S.), 8(3):285--322, 2013.
    Journal link. arXiv preprint.
  9. The energy of a smooth metric measure space and applications, J. Geom. Anal., 25(1):616--667, 2015.
    Journal link. arXiv preprint.
  10. (with Sagun Chanillo and Paul Yang) A remark on the kernel of the CR Paneitz operator, Nonlinear Analysis, 126:153--158, 2015.
    Journal link. arXiv preprint.
  11. A Yamabe-type problem on smooth metric measure spaces, J. Differential Geom., 101(3):467--505, 2015.
    Journal link. arXiv preprint.
  12. (with Sagun Chanillo and Paul Yang) The CR Paneitz operator and the stability of CR pluriharmonic functions, Adv. Math., 287:109--122, 2016.
    Journal link. arXiv preprint.
  13. (with Chin-Yu Hsiao and Paul Yang) Extremal metrics for the Q'-curvature, C. R. Math. Acad. Sci. Paris, 354(4):407--410, 2016.
    Announcment of arXiv:1511.05013.
    Journal link. arXiv preprint.
  14. (with Sun-Yung Alice Chang) On fractional GJMS operators, Comm. Pure Appl. Math., 69(6):1017--1061, 2016.
    Journal link. arXiv preprint.
  15. A notion of the weighted σk-curvature for manifolds with density, Adv. Math., 295:150--194, 2016.
    Journal link. arXiv preprint.
  16. A weighted renormalized curvature for manifolds with density, Proc. Amer. Math. Soc., 145:4031--4040, 2017.
    Journal link. arXiv preprint.
  17. Some energy inequalities involving fractional GJMS operators, Anal. PDE, 10(2):253--280, 2017.
    Journal link. arXiv preprint.
  18. Boundary operators associated to the Paneitz operator, Indiana Univ. Math. J., to appear.
    Early View journal link. arXiv preprint.
  19. (with Yi Wang) A Dirichlet principle for the k-Hessian, J. Funct. Anal., accepted.
    arXiv preprint.
  20. (with Chin-Yu Hsiao and Paul Yang) Extremal metrics for the Q'-curvature, J. Eur. Math. Soc., accepted.
    arXiv preprint.
Preprints
  1. (with Peng Wu) A generalization of the Cai--Galloway splitting theorem to smooth metric measure spaces, arXiv:1307.0848.
  2. The weighted σk-curvature of a smooth metric measure space, arXiv:1608.01663.
  3. (with Yi Wang) Boundary operators associated to the σk-curvature, arXiv:1707.04377.
  4. (with Jih-Hsin Cheng and Paul Yang) An integral formula for the Q-prime curvature in 3-dimensional CR geometry, arXiv:1709.05367.
  5. (with Rod Gover) The P'-operator, the Q'-curvature, and the CR tractor calculus, arXiv:1709.08057.
  6. (with Yueh-Ju Lin and Wei Yuan) Conformally variational Riemannian invariants, arXiv:1711.05579.