Jeff Viaclovsky: Preprints

Jeff Viaclovsky: Preprints Jeff Viaclovsky

Articles and Preprints

47. arXiv : Fibrations on the 6-sphere (with Nobuhiro Honda), 2024, 37 pages, preprint.

46. arXiv : Torelli-type theorems for gravitational instantons with quadratic volume growth (with Gao Chen and Ruobing Zhang), 2021, 41 pages, to appear in Duke Math. Journal.

45. Article : Conformally prescribed scalar curvature on orbifolds (with Tao Ju), Comm. Math. Phys. 398 (2023), no. 2, 877–923.

44. arXiv : Asymptotically Calabi metrics and weak Fano manifolds (with Hans-Joachim Hein, Song Sun, and Ruobing Zhang), 2021, 17 pages, preprint.

43. arXiv : Gravitational instantons with quadratic volume growth (with Gao Chen), 2021, 26 pages, to appear in Journal of the London Math. Soc.

42. Article : Hodge theory on ALG^* manifolds (with Gao Chen and Ruobing Zhang), J. Reine Angew. Math. 799 (2023), 189–277.

41. Article : Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces (with H.-J. Hein, S. Sun, and R. Zhang), J. Amer. Math. Soc. 35 (2021), no. 1, 123–209.

40. Article : Collapsing Ricci-flat metrics on elliptic K3 surfaces (with Gao Chen and Ruobing Zhang), Comm. Anal. Geom. 28 (2020), no. 8, 2019–2133.

39. Article : Existence and compactness theory for ALE scalar-flat Kähler surfaces (with Jiyuan Han), Forum Math. Sigma 8 (2020), Paper No. e1, 67 pages.

38. arXiv : Local moduli of scalar-flat Kähler ALE surfaces (with Jiyuan Han), 2018, Geometric Analysis - in Honor of Gang Tian's 60th Birthday, Progr. Math. 333 (2020), 113–135.

37. Article : The Calabi metric and desingularization of Einstein orbifolds (with Peyman Morteza), J. Eur. Math. Soc. 22 (2020), no. 4, 1201–1245.

36. Article : Deformation theory of scalar-flat Kähler ALE surfaces (with Jiyuan Han), Amer. J. Math. 141 (2019), no. 6, 1547–1589.

35. Article : Quotient singularities, eta invariants, and self-dual metrics (with Michael Lock), Geom. Topol. 20 (2016), no. 3, 1773–1806.

34. Article : A smorgasbord of scalar-flat Kähler ALE surfaces (with Michael Lock), J. Reine Agnew. Math. 746 (2019) 171–208.

33. Article : The mass of the product of spheres, Comm. Math. Phys. 335 (2015), no. 1, 17–41.

32. Article : Critical metrics on connected sums of Einstein four-manifolds (with Matt Gursky), Adv. Math. 292 (2016), 210–315.

31. Article : An index theorem for anti-self-dual orbifold-cone metrics (with Michael Lock), Adv. Math. 248 (2013), 698–716.

30. Article : Toric LeBrun metrics and Joyce metrics (with Nobuhiro Honda), Geom. Topol. 17 (2013), no. 5, 2923–2934.

29. Article : Einstein metrics and Yamabe invariants of weighted projective spaces, Tohoku Math. J. (2) 65 (2013), no. 2, 297–311.

28. Article : Anti-self-dual orbifolds with cyclic quotient singularities (with Michael Lock), J. Eur. Math. Soc. (JEMS) 17 (2015), no. 11, 2805–2841.

27. Article : An index theorem on anti-self-dual orbifolds, Int. Math. Res. Not. (IMRN) 2013, no. 17, 3911–3930.

26. Article : Asymptotics of the self-dual deformation complex (with Antonio Ache), Journal of Geometric Analysis 25 (2015), no. 2, 951–1000.

25. Article : Obstruction-flat asymptotically locally Euclidean metrics (with Antonio Ache), Geometric and Functional Analysis 22-4 (2012), 832–877.

24. Article : Rigidity and stability of Einstein metrics for quadratic curvature functionals (with Matt Gursky) , Crelle's Journal 700 (2015), 37–91.

23. Article : Monopole metrics and the orbifold Yamabe problem, Annales de L'Institut Fourier 60 (2010), no. 7, 2503–2543.

22. Article : Twistor geometry and warped product orthogonal complex structures (with Lev Borisov and Simon Salamon), Duke Math Journal 156 (2011), no. 1, 125–166.

21. Article : Conformal symmetries of self-dual hyperbolic monopole metrics (with Nobuhiro Honda), Osaka J. Math. 50 (2013), no. 1, 197–249.

20. Article : Threefolds of order one in the six-quadric (with Lev Borisov), Proc. Steklov Inst. Math. 264 (2009), no. 1, 18–29.

19. Article : Orthogonal complex structures on domains in R^4 (with S. Salamon), Math. Annalen 343, no. 4, 2009, 853–899.

18. Article : Volume growth, curvature decay, and critical metrics (with G. Tian), Comm. Math. Helv. 83, Issue 4, 2008, pages 889–911.

17. pdf : Conformal geometry and fully nonlinear equations, Inspired by S. S. Chern, Nankai Tracts Math 11, World Scientific, 2006, pages 435–460.

16. Article : Convexity and singularities of curvature equations in conformal geometry (with M. Gursky), IMRN 2006: article ID 96890, 43 pages.

15. Article : Prescribing symmetric functions of the eigenvalues of the Ricci tensor (with M. Gursky), Annals of Mathematics 166 (2007) no. 2, 475–531.

14. Article : Moduli spaces of critical Riemannian metrics in dimension four (with G. Tian), Advances in Mathematics 196 (2005) no. 2, 346–372.

13. Article : Bach-flat asymptotically locally Euclidean metrics (with G. Tian), 2003, Inventiones Mathematicae 160 (2005) no. 2, 357–415.

12. Article : A fully nonlinear equation on four-manifolds with positive scalar curvature (with M. Gursky), Journal of Differential Geometry 63, no. 1, 2003, 131–154.

11. Article : Volume comparison and the sigma_k-Yamabe problem (with M. Gursky), Advances in Mathematics 187 (2004), no. 2, 447–487.

10. Article : Fully nonlinear equations on Riemannian manifolds with negative curvature (with M. Gursky), Indiana Univ. Math. J. 52 (2003), no. 2, 399–420.

9. Article : A variational characterization for sigma_{n/2} (with S. Brendle), Calc. Var. PDE. 20 (2004), no. 4, 399–402.

8. Article : Some properties of the Schouten tensor and applications to conformal geometry (with P. Guan and G. Wang), Trans. Amer. Math. Soc. 355 (2003), no. 3, 925–933.

7. Article : Estimates and Existence Results for some Fully Nonlinear Elliptic Equations on Riemannian Manifolds, Communications in Analysis and Geometry 10 (2002), no.4, 815–846.

6. Article : On the regularity of solutions to Monge-Ampere equations on Hessian manifolds, (with L. Caffarelli), Comm. PDE 26 (2001), no. 11–12, 2339–2351.

5. Article : A new variational characterization of three-dimensional space forms (with M. Gursky), Invent. Math. 145 (2001) 2, 251–278.

4. Article : Regularity of weak solutions to critical exponent variational equations (with K. Uhlenbeck), Math. Res. Lett. 7 (2000), no. 5–6, 651–656.

3. dvi or ps : Some Fully Nonlinear Equations in Conformal Geometry, Differential equations and mathematical physics (Birmingham, AL, 1999) (Providence, RI), Amer. Math. Soc., Providence, RI, 2000, pp. 425–433.

2. Article : Conformal Geometry, Contact Geometry and the Calculus of Variations, Duke Math. J. 101 (2000), no. 2, 283–316.

1. Article : Conformally Invariant Monge-Ampere Partial Differential Equations: Global Solutions, Trans. Amer. Math. Soc. 352 (2000), no. 9, 4371–4379.

Contact Information

@

uci.edu