Skip to main content
SpringerLink
Log in

Singularities of Special Lagrangian Submanifolds

  • Chapter
Different Faces of Geometry

Part of the book series: International Mathematical Series ((IMAT,volume 3))

Supported by an EPSRC Advanced Research Fellowship.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.E. Bredon, Topology and Geometry, Graduate Texts in Mathematics 139, Springer-Verlag, Berlin, 1993.

    Google Scholar 

  2. R. Harvey, Spinors and Calibrations, Academic Press, San Diego, 1990.

    MATH  Google Scholar 

  3. R. Harvey and H. B. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47–157.

    MathSciNet  MATH  Google Scholar 

  4. M. Haskins, Special Lagrangian Cones, math.DG/0005164, 2000. [To appear in Am. J. Math.]

    Google Scholar 

  5. M. Haskins, The geometric complexity of special Lagrangian T 2-cones, math.DG/0307129, 2003. [To appear in Invent. Math.]

    Google Scholar 

  6. D. D. Joyce, On counting special Lagrangian homology 3-spheres, pages 125–151 in Topology and Geometry: Commemorating SISTAG, editors A.J. Berrick, M.C. Leung and X.W. Xu, Contemporary Mathematics 314, Am. Math. Soc., Providence, RI, 2002. hep-th/9907013, 1999.

    Google Scholar 

  7. D. D. Joyce, Special Lagrangian m-folda in C m with symmetries, Duke Math. J. 115 (2002), 1–51. math.DG/0008021.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. D. Joyce, Constructing special Lagrangian m-joldt in C m by evolving quadrics, Math. Ann. 320 (2001), 757–797. math.DG/0008155.

    MATH  MathSciNet  Google Scholar 

  9. D. D. Joyce, Evolution equations for special Lagrangian 3-folds in C 3, Ann. Global Anal. Geom. 20 (2001), 345–403. math.DG/0010036.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. D. Joyce, Singularities of special Lagrangian fibrations and the SYZ Conjecture, Comm. Anal. Geom. 11 (2003), 859–907. math.DG/0011179.

    MATH  MathSciNet  Google Scholar 

  11. D. D. Joyce, Ruled special Lagrangian 3-folds in C 3, Proc. London Math. Soc. 85 (2002), 233–256. math.DG/0012060.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. D. Joyce, Special Lagrangian 3-folds and integrable systems, math.DG/0101249, 2001. [To appear in volume 1 of the Proceedings of the Mathematical Society of Japan’s 9th International Research Institute on Integrable Systems in Differential Geometry, Tokyo, 2000.]

    Google Scholar 

  13. D. D. Joyce, Lectures on Calabi-Yau and special Lagrangian geometry, math.DG/0108088, 2001. Published, with extra material, as Part I of M. Gross, D. Huybrechts and D. Joyce, Calabi-Yau Manifolds and Related Geometries, Universitext series, Springer, Berlin, 2003.

    Google Scholar 

  14. D. D. Joyce, U(1)-invariant special Lagrangian 3-folds. I. Nonsingular solutions, math.DG/0111324, 2001. [To appear in Adv. Math.]

    Google Scholar 

  15. D. D. Joyce, U(1)-invariant special Lagrangian 3-folds. II. Existence of singular solutions, math.DG/0111326, 2001. [To appear in Adv. Math.]

    Google Scholar 

  16. D. D. Joyce, U(1)-invariant special Lagrangian 3-folds. III. Properties of singular solutions, math.DG/0204343, 2002. [To appear in Adv. Math.]

    Google Scholar 

  17. D. D. Joyce, U(1)-invariant special Lagrangian 3-folds in C 3 and special Lagrangian fibrations, Turkish Math. J. 27 (2003), 99–114. math.DG/0206016.

    MATH  MathSciNet  Google Scholar 

  18. D. D. Joyce, Special Lagrangian submanifolds with isolated conical singularities. I. Regularity, Ann. Global Anal. Geom. 25 (2004), 201–251. math.DG/0211294.

    MATH  MathSciNet  Google Scholar 

  19. D. D. Joyce, Special Lagrangian submanifolds with isolated conical singularities. II. Moduli spaces, Ann. Global Anal. Geom. 25 (2004), 301–352. math.DG/0211295.

    MATH  MathSciNet  Google Scholar 

  20. D. D. Joyce, Special Lagrangian submanifolds with isolated conical singularities III. Desingularization, the unobstructed case, Ann. Global Anal. Geom. 26 (2004), 1–58. math.DG/0302355.

    MATH  MathSciNet  Google Scholar 

  21. D. D. Joyce, Special Lagrangian submanifolds with isolated conical singularities. IV. Desingularization, obstructions and families, math.DG/0302356, 2003. [To appear in Ann. Global Anal. Geom.]

    Google Scholar 

  22. O.D. Joyce, Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applications, J. Differ. Geom. 63 (2003), 279–347. math.DG/0303272.

    MATH  MathSciNet  Google Scholar 

  23. G. Lawlor, The angle criterion, Invent. Math. 95 (1989), 437–446.

    Article  MATH  MathSciNet  Google Scholar 

  24. R. Lockhart, Fredholm, Hodge and Liouville Theorems on noncompact manifolds, Trans. Am. Math. Soc. 301 (1987), 1–35.

    MathSciNet  Google Scholar 

  25. S. P. Marshall, Deformations of special Lagrangian submanifolds, Oxford D. Phil. Thesis, 2002.

    Google Scholar 

  26. D. McDuff and D. Salamon, Introduction to symplectic topology, second ed., Oxford University Press, Oxford, 1998.

    MATH  Google Scholar 

  27. I, McIntosh, Special Lagrangian cones in C 3 and primitive harmonic maps, J. London Math. Soc. 67 (2003), 769–789. math.DG/0201157.

    Article  MATH  MathSciNet  Google Scholar 

  28. R. C. McLean, Deformations of calibrated submanifolds, Comm. Anal. Geom. 6 (1998), 705–747.

    MATH  MathSciNet  Google Scholar 

  29. F. Morgan, Geometric Measure Theory, A Beginner’s Guide, Academic Press, San Diego, 1995.

    MATH  Google Scholar 

  30. T. Pacini, Deformations of Asymptotically Conical Special Lagrangian Submanifolds, math.DG/0207144, 2002.

    Google Scholar 

  31. A. Strominger, S.-T. Yau, and E. Zaslow, Mirror symmetry is T-duality, Nucl. Phys. B479 (1996), 243–259. hep-th/9606040.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lincoln College, Oxford, UK

    Dominic Joyce

Authors
  1. Dominic Joyce
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Imperial College of London, London, UK

    Simon Donaldson

  2. Stanford University, Stanford, California

    Yakov Eliashberg

  3. Institut des Haute Etudes Scientifiques, Bures-sur-Yvette, France

    Mikhael Gromov

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science + Business Media, Inc.

About this chapter

Cite this chapter

Joyce, D. (2004). Singularities of Special Lagrangian Submanifolds. In: Donaldson, S., Eliashberg, Y., Gromov, M. (eds) Different Faces of Geometry. International Mathematical Series, vol 3. Springer, Boston, MA. https://doi.org/10.1007/0-306-48658-X_4

Download citation

  • DOI: https://doi.org/10.1007/0-306-48658-X_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-48657-9

  • Online ISBN: 978-0-306-48658-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation