A Spinorial Approach to Riemannian and Conformal Geometry
(with Jean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, and Andrei Moroianu, 458 pages),
EMS Monographs in Mathematics, 2015.

Papers and preprints

  1. Concentration limit for non-local dissipative convection-diffusion kernels on the hyperbolic space, [pdf], (with Maria Del Mar González, Liviu Ignat and Dragoş Manea), arXiv:2302.02624.
  2. Cauchy spinors on 3-manifolds, [pdf], (with Brice Flamencourt), J. Geom. Analysis 32 (2022), article 186, arXiv:2110.15386.
  3. Higher transgressions of the Pfaffian, [pdf], arXiv:2011.06538, Revista Matemática Iberoamericana 38, no.5, 1425-1452 (2022).
  4. Odd Pfaffian forms, [pdf], (with Daniel Cibotaru), arXiv:1807.00239, Bull. Brazilian Math. Soc. 52 (2021), 915-976.
  5. Locally conformally Kähler manifolds with holomorphic Lee field [pdf] (with Andrei Moroianu and Liviu Ornea), Differential Geom. Appl. 60 (2018), 33-38.
  6. On pluricanonical locally conformally Kähler manifolds [pdf] (with Andrei Moroianu), arXiv:1512.04318, Int. Math. Res. Not. 2017 no. 14 (2017), 4398-4405.
  7. The Cotton tensor and Chern-Simons invariants in dimension 3: an introduction [pdf], arXiv:1509.05156, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 78 no. 2 (2015), 3-20.
  8. Boundaries of locally conformally flat manifolds in dimensions 4k [pdf], preprint arXiv:1506.05968, Indiana University Mathematics Journal 67 no. 1 (2018), 329-342.
  9. Renormalized volume on the Teichmüller space of punctured surfaces [pdf] (with Colin Guillarmou and Frédéric Rochon), arXiv:1503.07981, Ann. Sc. Norm. Super. Pisa, Cl. Sci. 17 (2017), 323-384.
  10. Convexity of the renormalized volume of hyperbolic 3-manifolds [pdf], preprint arXiv:1503.07981, Amer J. Math. 139 no. 5 (2017), 1379-1394.
  11. Positivity of the renormalized volume of almost-Fuchsian hyperbolic 3-manifolds [pdf] (with Corina Ciobotaru), arXiv:1402.2555, Proc AMS 144 (2016), 151-159.
  12. The renormalized volume and uniformisation of conformal structures [pdf] (with Colin Guillarmou and Jean-Marc Schlenker), J. Math. Jussieu 17, no. 4 (2018), 853-912.
  13. Ricci surfaces [pdf] (with Andrei Moroianu), preprint arXiv:1206.1620, Ann. Sc. Norm. Super. Pisa Cl. Sci. 14, no. 4 (2015), 1093-1118.
  14. The Cauchy problem for Einstein metrics and parallel spinors [pdf] (with Bernd Ammann and Andrei Moroianu), Commun. Math. Phys. 320 (2013), 173-198.
  15. Chern-Simons line bundle on Teichmüller space [pdf] (with Colin Guillarmou), Geometry & Topology 18, no. 1 (2014), 327-377.
  16. Uniformization of S2 and flat singular surfaces [pdf], preprint arXiv:1101.2355.
  17. Bergman and Calderón projectors for Dirac operators [pdf] (with Colin Guillarmou and Jinsung Park), J. Geom. Analysis 24, no. 1 (2014), 298-336.
  18. On the singularities of the zeta and eta functions of an elliptic operator [pdf] (with Paul Loya and Raphaël Ponge), Int. J. Math. 23, no. 6 (2012), 1250020.
  19. The spectrum of k-form Schrödinger Laplacians on conformally cusp manifolds [pdf] (with Sylvain Golénia), Trans. Amer. Math. Soc. 364 (2012), 1-29.
  20. Regularity of the eta function on manifolds with cusps [pdf] (with Paul Loya and Jinsung Park), Mathematische Zeitschrift 269 (2011), no. 3-4, 955-975.
  21. The Dirac operator on generalized Taub-NUT spaces [pdf] (with Andrei Moroianu), Comm. Math. Phys. 305 (2011), 641-656.
  22. Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds [pdf] (with Colin Guillarmou and Jinsung Park), Advances in Mathematics 225, no. 5 (2010), 2464-2516.
  23. Quasi-fuchsian manifolds with particles [pdf] (with Jean-Marc Schlenker), J. Differential Geometry 83 (2009), 75-129.
  24. Adiabatic limit of the eta invariant over cofinite quotients of PSL(2,R) [pdf] (with Paul Loya and Jinsung Park), Compositio Math. 144 (2008), 1593-1616.
  25. Spectral analysis of magnetic Laplacians on conformally cusp manifolds [pdf] (with Sylvain Golénia), Ann. Henri Poincaré 9 (2008), 131-179.
  26. Weyl laws on open manifolds [pdf], Math. Annalen 340 (2008), 1-21.
  27. Index and homology of pseudodifferential operators on manifolds with boundary [pdf] (with Victor Nistor), Perspectives Oper. Algebras Math. Phys., Theta (2008), 123-148.
  28. The Dirac spectrum on manifolds with gradient conformal vector fields [pdf] (with Andrei Moroianu), J. Funct. Analysis 253 (2007), 207-219.
  29. Fibered cusp versus d-index theory [pdf], Rend. Semin. Mat. Padova 117 (2007), 193-203.
  30. On the structure of quantum permutation groups [pdf] (with Teodor Banica), Proc. Amer. Math. Soc. 135 (2007), 21-29.
  31. On Carvalho's K-theoretic formulation of the cobordism invariance of the index [pdf], Proc. Amer. Math. Soc. 134 (2006), 3395-3404.
  32. L2-index of the Dirac operator of generalized Euclidean Taub-NUT metrics [pdf] (with Mihai Vişinescu), J. Phys. A - Math. Gen. 39 (2006), 6575-6581.
  33. On the Lp index of spin Dirac operators on conical manifolds [pdf] (with André Legrand), Studia Math. 177 (2006), 97-112.
  34. Gravitational and axial anomalies for generalized Euclidean Taub-NUT metrics [pdf] (with Ion Cotăescu and Mihai Vişinescu), J. Phys. A - Math. Gen. 38 (2005), 7005-7019.
  35. An index formula on manifolds with fibered cusp ends [pdf] (with Robert Lauter), J. Geom. Analysis 15 (2005), 261-283.
  36. Cusp geometry and the cobordism invariance of the index [pdf], Advances in Math. 194 (2005), 504-519.
  37. Homology of adiabatic pseudo-differential operators [dvi], Nagoya Math. J. 175 (2004), 171-221.
  38. Adiabatic limits of eta and zeta functions of elliptic operators [ps], Math. Zeitschrift 246 (2004), 441-471.
  39. Heat Kernel Asymptotics for Roots of Generalized Laplacians [ps] (with Christian Bär), Int. J. Math. 14 (2003), 397-412.
  40. K-Theory of suspended pseudo-differential operators [ps], K-Theory 28 (2003), 167-181.
  41. Homology of pseudodifferential operators on manifolds with fibered cusps [dvi] (with Robert Lauter), Trans. Amer. Math. Soc. 355 (2003), 3009-3046.
  42. Sur la limite adiabatique des fonctions eta et zeta [dvi], C. R. Acad. Sci. I-Math. 334 (2002), 131-134.
  43. The index of cusp operators on manifolds with corners [dvi] (with Robert Lauter), Ann. Global Anal. Geom. 21 no. 1 (2002), 31-49.
  44. Homology of pseudo-differential operators on manifolds with fibered boundaries [dvi] (with Robert Lauter), J. Reine Angew. Math. 547 (2002), 207-234.
  45. Fredholm Theory for degenerate pseudodifferential operators on manifolds with fibered boundaries [dvi] (with Robert Lauter), Comm. Partial Diff. Equations 26 (2001), 233-285.
  46. On the index formula of Melrose and Nistor [dvi] (with Robert Lauter), IMAR preprint 3/2000.
  47. Thesis [ps] and my former PhD advisor Richard B. Melrose.

 modificat ultima dată: 16 martie 2022
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