Publications

  • Adiabatic limits, the non-multiplicativity of signature and Leray spectral sequence, Journal of A. M. S. vol 4 (1991), pp 256-321. pdf file
  • Geometric invariants and their adiabatic limits. 145--156, Proc. Sympos. Pure Math., 54, Part 2, Amer. Math. Soc., Providence, RI, 1993. pdf file
  • Eta invariants and determinant lines, J. Math. Phys., 35(1994), 5155-5194. with Dan Freed pdf file
  • Negative Ricci curvature and isometry group, Duke Math J., 76(1994), 59-73. with Zhongmin Shen and Guofang Wei pdf file
  • Finite part of the spectrum and isospectrality, Contemp. Math 173(1994), pp. 99-107 with Guofang Wei pdf file
  • The Atiyah-Patodi-Singer index theorem: a proof via embedding, C. R. Acad. Sci, Paris, Series I, 319(1994), pp 1293-1297. with Weiping Zhang pdf file
  • Invariants eta et droites determinants, C. R. Acad. Sci., Paris, Series I, 320(1995), pp 585-591. with Dan Freed pdf file
  • Circle bundles and the Kreck-Stolz invariant, Trans. A. M. S., 347(1995), pp 3587-3593. with Weiping Zhang pdf file
  • A Toponogov type comparison estimate for the Ricci curvature, Math. Ann. 303(1995), 297-306. with Guofang Wei pdf file
  • Higher spectral flows, Math. Res. Letters 3(1996), 93-102. with Weiping Zhang pdf file
  • Smoothing Riemannian metrics with Ricci curvature bounds, Manu. Math. 90(1996), 46-61. with Guofang Wei and Rugang Ye pdf file
  • Splitting of the family index, Comm. Math. Phys. 182(1996), pp 303-317. with Weiping Zhang pdf file
  • Higher spectral flows, J. Funct. Anal. 157(1998), pp 432-469. with Weiping Zhang pdf file
  • Analytic torsion and R-torsion for manifolds with boundary, Asian J. Math. 4(2000), pp695-714. with Hao Fang pdf file
  • Integral Pinching Theorems, Manu. Math. 101(2000), pp143-152. with Peter Petersen and Guofang Wei pdf file
  • Real embeddings and the Atiyah-Patodi-Singer index theorem for Dirac operators, Asian J. Math. 4(2000), pp775-794. with Weiping Zhang pdf file
  • APS boundary conditions, eta invariants and adiabatic limits, Trans. AMS, 354(2002), pp107-122. pdf file
  • A heat kernel lower bound for integral Ricci curvature, Michigan J. Math. 52(2004), pp61-69. with Guofang Wei pdf file
  • A Positive Mass Theorem for Spaces with Asymptotic SUSY Compactification, Comm. Math. Phys., 244(2004), 335-345. pdf file
  • On the asymptotic expansion of Bergman kernel, C. R. Acad. Sci, Paris, Series I 339(2004), 193-198. with Kefeng Liu and Xiaonan Ma pdf file
  • A Note on Positive Energy Theorem for Spaces with Asymptotic SUSY Compactification, Journal of Mathematical Physics, 46(2005), 042505-1 -- -7. pdf file
  • Eta invariant and conformal cobordism, Annals of Global Analysis and Geometry, 27(2005), 333-340. pdf file
  • On the Stability of Riemannian Manifold with Parallel Spinors, Invent. Math. 161(2005), 151-176. with Xiaodong Wang and Guofang Wei pdf file
  • On the asymptotic expansion of Bergman kernel, Journal of Differential Geometry 72(2006), 1-41. with Kefeng Liu and Xiaonan Ma pdf file
  • Eta invariants for manifold with boundary, Analysis, Geometry and Topology of Elliptic Operators, World Scientific and Imperial College Press, 2006, 141-172 pdf file
  • An index theorem for Toeplitz operators on odd dimensional manifolds with boundary, J. Funct. Anal. 238 (2006), no. 1, 1--26. with Weiping Zhang pdf file
  • Hitchin-Thorpe Inequality for Noncompact Einstein $4$-Manifolds, Advance in Math. 214 (2007) , no. 2, 551-570. with Guofang Wei pdf file
  • Mass under the Ricci flow, Comm. Math. Phys. 274 (2007), 65-80. with Li Ma pdf file
  • On the variational stability of Kahler-Einstein metrics, Comm. Anal. Geom. 15 (2007), 669-693. with Xiaodong Wang and Guofang Wei pdf file
  • Stability of Einstein metrics and spin structures, Proceedings of the 4th International Congress of Chinese Mathematicians (2007), Vol. II, 59-72. pdf file
  • $L^2$-cohomology of Spaces of Non-isolated Conical Singularity and Non-multiplicativity of signature, Progress in Mathematics (2009), 271 Birkh\"auser, 1-24. with Jeff Cheeger pdf file
  • Adiabatic limit, Bismut-Freed connection and real analytic torsion form, Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal), 2010. with Weiping Zhang pdf file
  • An Introduction to L2 Cohomology,  Topology of Stratified Spaces, MSRI Publications, vol. 58,  2010. pdf file
  • Adiabatic limit, heat kernels and analytic torsions, Progress in Mathematics, Vol 297 Birhauser， 233-298。 with Richard Melrose pdf file
  • A remark on weighted Bergman kernel on orbifolds, Math Research Letters, 19 (2012), no. 01, 1�6. with K. Liu and X. Ma pdf file
  • Eta invariants for even dimensional manifolds, Fifth International Congress of Chinese Mathematicians. Part 1, 2, 51�60, AMS/IP Stud. Adv. Math., 51, pt. 1, 2, Amer. Math. Soc., Providence, RI, 2012. pdf file
  • Eta Invariant and Holonomy: the even dimensional case, Adv. In Math. 279(2015), 291-306. with W. Zhang pdf file
  • Comparison between two analytic torsions on orbifolds, Math Z.(2017) 285:1269�1282 with J. Yu pdf file
  • Local Sobolev constant estimate for integral Ricci curvature bounds, Adv. in Math. 325 (2018), 1-33.  with G. Wei and Z. Zhang pdf file
  • Neumann isoperimetric constant estimate for convex domains, Proc. AMS, 146 (2018), no. 8, 3509-3514. with G. Wei and Z. Zhang pdf file
  • Perelman�s $\lambda$-functional for Manifolds with Conical Singularities, J. Geom. Anal. (2018)28, 3657�3689, with C. Wang pdf file
  • Fundamental gap comparison; Survey in Geometric Analysis 2018, (2019) 1-16, with S. Seto, G. Wei pdf file
  • Perelman's W-functional on manifolds with conical singularities, MRL 27(2020), 665-685, with C. Wang pdf file
  • Gromov rigidity of bi-invariant metrics on Lie groups and homogeneous spaces, SIGMA 16(2020), 068 (Special issue for Gromov's 75th Birthday), with Y. Sun pdf file
  • Fundamental gap estimate for convex domains on sphere -- the case n=2,  Comm. Anal. Geom. 29(2021), 1095-1125, with S. Seto, G. Wei pdf file
  • Witten deformation on noncompact manifolds with bounded geometry, J. Institute Math. Jussieu (2021), 1-38, with J. Yan pdf file
  • Maximal volume entropy rigidity for $\mathsf{RCD}^*(-(N-1),N)$ spaces, J. London Math. Soc. 104(2021), 1615-1681, with C. Connell, J. N\'u\~nez-Zimbr\'on, R. Perales, P. Su\'arez-Serrato, G. Wei pdf file
  • Analytic torsion for log-Enriques surfaces and Borcherds product, Forum Math. Sigma. 10(2022), Paper No. e77, 54pp, with K. Yoshikawa pdf file
  • Witten deformation on noncompact manifolds: heat kernel and local index theorem, Math. Z., 303(2023),no. 1, Paper No. 5， 28pp, with J. Yan pdf file
  • Asymptotic spectral flow, Math. Z., 303(2023),no. 1, Paper No. 78， 39pp, with Y. Li pdf file
  • Compactification and positive mass theorem for fibered Euclidean end, Journal of Geometric Analysis, 33(2023), no.9, Paper No. 275， 26pp, with Y. Sun pdf file
  • Singular Weyl's law with Ricci curvature bounded below, Trans. AMS, Series B, 10(2023), 1212-1253, with S. Honda, J. Pan, G. Wei pdf file
  • Perelman's functionals on manifolds with non-isolated conical singularities, Calc. Var. Partial Differential Equations 63 (2024), no. 9, Paper No. 233, 51 pp. with C. Wang pdf file
  • Positive mass theorem for asymptotically flat spin manifolds with isolated conical singularities, to appear in Trans. AMS, Series B. with Y. Sun, C. Wang pdf file

    • Preprints

    The intersection R-torsion of a finite cone,  with Xiaoling Huang pdf file

    Volume entropy and rigidity for RCD-spaces,  arXiv:2411.04327 with C. Connell, J. N\'u\~nez-Zimbr\'on, R. Perales, P. Su\'arez-Serrato, G. Wei pdf file

    Positive scalar curvature and isolated conical singularity,  arXiv:2412.02941 with Y. Sun, C. Wang pdf file

      Singular metrics with nonnegative scalar curvature and RCD, arXiv:2412.09185 with C. Wang, L. Wang, G. Wei pdf file


    Books and Lecture Notes

  • Metric and Differential Geometry, the Jeff Cheeger Anniversary Volume. Progress in Mathematics, Vol 297 Birhauser. Co-edited with X. Rong
  • From probability to geometry (I), Volume in honor of the 60th Birthday of Jean-Michel Bismut， Asterique, vol. 327, 1-424. Co-edited with Remi Leandre, Xiaonan Ma and Weiping Zhang.
  • From probability to geometry (II), Volume in honor of the 60th Birthday of Jean-Michel Bismut， Asterique, vol. 328, 1-393. Co-edited with Remi Leandre, Xiaonan Ma and Weiping Zhang.
  • Lectures On Dirac Operators And Index Theory pdf file
  • Comaprison Geometry for Ricci Curvature, with Guofang Wei pdf file