Zhizhang Xie

Publications

  1. (With J. Wang, G. Yu and B. Zhu) ℓp-coarse Baum--Connes conjecture for ℓq-coarse embeddable spaces
  2. (With J. Wang) Scalar curvature rigidity of spheres with subsets removed and L∞ metrics
  3. (With S. Cecchini, J. Wang and B. Zhu) Scalar curvature rigidity of the four-dimensional sphere
  4. (With J. Wang, G. Yu and B. Zhu) Filling Radius, Quantitative K-theory and Positive Scalar Curvature
  5. (With G. Tian and G. Yu) On the relative Novikov conjecture for coarsely embeddable groups
  6. (With S. Gong, J. Wu and G. Yu) The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces
  7. (With J. Wang) Dihedral rigidity for submanifolds of warped product manifolds
  8. (With J. Wang) On Gromov's flat corner domination conjecture and Stoker's conjecture
  9. (With J. Wang and G. Yu) On Gromov's dihedral extremality and rigidity conjectures
  10. (With J. Wang) Scalar curvature rigidity of degenerate warped product spaces, Trans. Amer. Math. Soc. Ser. B 12 (2025), 1-37.
  11. (With J. Wang, B. Zhu and X. Zhu) Positive scalar curvature meets Ricci limit spaces, Manuscripta Math. 175 (2024), no. 3-4, 943-969.
  12. (With S. Weinberger and G. Yu) On Gromov's compactness question regarding positive scalar curvature, Ann. K-Theory 9 (2024), no. 4, 583-612.
  13. (With J. Deng, G. Tian and G. Yu) K-theory of relative group C*-algebras and the relative Novikov conjecture, Math. Z. 306 (2024), no.3, Paper No. 45, 38 pp.
  14. (With J. Wang and G. Yu) A proof of Gromov's cube inequality on scalar curvature, J. Differential Geom. Vol. 128, No. 3 (2024), pp. 1285-1300.
  15. (With J. Wang and G. Yu) Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension, Comm. Pure Appl. Math. 77 (2024), no. 1, 372–440.
  16. (with Hongzhi Liu and G. Yu) Equivalence of different definitions of higher ρ invariants, Scientia Sinica Mathematica, Volume 53 , Issue 12: 1713 (2023)
  17. (with X. Chen, J. Wang and G. Yu) Delocalized eta invariants, cyclic cohomology and higher rho invariants, Ann. K-Theory 8 (2023), no. 4, 531–608.
  18. (with J. Wang and G. Yu) ℓ1 higher index, ℓ1 higher rho invariant and cyclic cohomology, Cyclic Cohomology at 40: Achievements and Future Prospects, Proc. Sympos. Pure Math., Vol. 105, 535–579, 2023
  19. A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature, Journal of Noncommutative Geometry 17 (2023), no. 2, 609–662.
  20. (With H. Guo and G. Yu) Quantitative K-theory, positive scalar curvature, and band width, Perspectives on Scalar Curvature (edited by Gromov and Lawson) Vol. 2, 763–798, World Sci. Publ., 2023
  21. (With J. Wang and G. Yu) Approximations of delocalized eta invariants by their finite analogues, L'Enseignement mathématique, 69 (2023), no. 1-2, 51–91.
  22. (with H. Guo and G. Yu) A Lichnerowicz vanishing theorem for the maximal Roe algebra, Math. Ann. 385 (2023), no. 1-2, 717–743.
  23. (with G. Yu and R. Zeidler) On the range of the relative higher index and the higher rho-invariant for positive scalar curvature, Adv. Math. 390 (2021), Paper No. 107897, 24 pp
  24. (With H. Guo and G. Yu) Functoriality for higher rho invariants of elliptic operators, J. Funct. Anal. 280 (2021), no. 10, Paper No. 108966, 36 pp
  25. (with G. Yu) Delocalized eta invariants, algebraicity, and K-theory of group C*-algebras, Int. Math. Res. Not. IMRN, (2021), no. 15, 11731–11766.
  26. (with S. Weinberger and G. Yu) Additivity of higher rho invariants and nonrigidity of topological manifolds, Comm. Pure Appl. Math. 74 (2021), no. 1, 3–113.
  27. (with G. Yu) Higher Invariants in Noncommutative Geometry - On the Occasion of Alain Connes' 70th Birthday, Advances in Noncommutative Geometry, Springer, 2019
  28. (with A. Gorokhovsky) Fibrations and higher products in cohomology, Journal of Topology and Analysis, 11 (2019), no. 1, 135–147.
  29. (with A. Gorokhovsky and D. Sullivan)  Generalized Euler classes, differential forms and commutative DGAs, Journal of Topology and Analysis, 11 (2019), no. 1, 109–118.
  30. (with N. Higson ) Higher signatures on Witt spaces
  31. (with N. Higson and T. Schick) On C*-Algebraic Higher Signatures and an Invariance Theorem in Codimension Two, Geom. Topol. 22 (2018) no.6, 3671–3699
  32. (with G. Yu) Higher rho invariants and the moduli space of positive scalar curvature metrics, Advances in Mathematics 307 (2016), 1046–1069
  33. (with G. Yu) Noncommutative Geometry of Discrete Groups, Introduction to modern mathematics, 425 - 432, Adv. Lect. Math. (ALM) 33, 2015.
  34. (with G. Yu) Positive scalar curvature, higher rho invariants and localization algebras, Advances in Mathematics 262 (2014), 823–866.
  35. (with G. Yu) A relative higher index theorem, diffeomorphisms and positive scalar curvature, Advances in Mathematics, 250 (2014), 35–73.
  36. The odd dimensional analogue of a theorem of Getzler and Wu, Journal of Noncommutative Geometry, 7 (2013), no. 3, 647–676.
  37. Relative index pairing and odd index theorem for even dimensional manifolds, Journal of Functional Analysis, 260 (2011), no. 7, 2064–2085