Skip to main content
Log in

The Thullen type extension theorem for holomorphic vector bundles withL 2-bounds on curvature

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Atiyah, M.F.: The geometry of Yang-Mills fields. Fermi lectures. Scuola normale, Pisa, 1977

    Google Scholar 

  2. Bando, S.: Removable singularities for holomorphic vector bundles. Tôhoku Math. J.43 (1991), 61–67

    Google Scholar 

  3. Federer, H.: Geometric measure theory. Springer-Verlag, 1969

  4. Forgács, P., Horváth, Z., Palla, L.: An exact fractionally charged self-dual solution. Phys. Rev. Lett.46 (1981), 392

    Google Scholar 

  5. Forgács, P., Hováth, Z., Palla, L.: One can have noninteger topological charge. Z. Phys. C—Particles and Fields12 (1982), 359–360

    Google Scholar 

  6. Gilbarg, D., Trudinger, N.: Elliptic partial differential equation of second order. 2nd ed., Springer-Verlag, Berlin (1983)

    Google Scholar 

  7. Griffiths, P., Harris J.: Principles of algebraic geometry. Wiley, New York, 1978

    Google Scholar 

  8. Harvey, R., Polking, J. C.: Removable singularities of solutions of partial differential equations. Acta Math.125 (1970), 209–226

    Google Scholar 

  9. Hörmander, L.: An introduction to complex analysis in several variables. D. van Nostrand, Co., Princeton, New Jersey, 1966

    Google Scholar 

  10. Ivashkovich, S.M.: An extension theorem of Thullen type for line bundles withL 2-bounded curvature. Soviet Math. Dokl.38 (1989), 516–518

    Google Scholar 

  11. Ivashkovich, S.M., together with Ajzenberg L. et al.: Some open problems in complex analysis of several variables, in Russian Preprint No 41M (1987), Physical Institute of L.V. Kirensky, Krasnoyarks, USSR (in Russian)

    Google Scholar 

  12. Jaffe, A., Taubes, C.: Vortices and monopoles. Birkhäuser, Boston, MA, 1984

    Google Scholar 

  13. King, J.: The currentsdefined by analytic varieties. Acta Math.127 (1971), 185–220

    Google Scholar 

  14. Kobayashi, S., Nomizu, K.: Foundations of differential geometry. Wiley, New York, 1969

    Google Scholar 

  15. Kronheimer, P.B.: Imbedded surfaces in 4-manifolds. Proc. Int. Congr. Math., Kyoto, Japan, 1990, Vol. 1, 529–539

    Google Scholar 

  16. Kronheimer, P.B.: The genus-minimizing property of algebraic curves. Bull. AMS29 (1993), 63–69

    Google Scholar 

  17. Malgrange, B.: Lectures on the theory of functions of several complex variables. Tata Ins. Fund. Res., Bombay, 1958

    Google Scholar 

  18. Matsushima, Y.: Espaces homogènes de Stèin des groupes de Lie complex. Nagoya Math. J.16 (1960), 205–218

    Google Scholar 

  19. Morrey, C.B.: Multiple integral in the calculus of variations. Springer-Verlag, Berlin, 1966

    Google Scholar 

  20. Okonek, Ch., Schneider, M., Spindler, H.: Vector Bundles on Complex Projective Spaces. Birkhäuser, Boston, MA, 1980

    Google Scholar 

  21. Onishchik, A.L.: Complex hulls of compact homogeneous spaces. Doklady Ac. of Sci. USSR130 (1960), 726–729

    Google Scholar 

  22. Rothstein, W.: Ein neuer Beweis des Hartogsschen Hauptsatzes und seine Ausdehnung auf meromorphe Funktionen. Math. Z.53 (1950), 84–95

    Google Scholar 

  23. Shevchishin, V.V.: The Oka-Grauert principle for the extension of holomorphic line bundles with integrable curvature. Math. Notes50 (1991), 1170–1177

    Google Scholar 

  24. Shevchishin, V.V.: Cohomological obstructions for extension of holomorphic line bundles. Math. Methods and Phys.-Mech. Fields34 (1991), 4–7 (in Russian)

    Google Scholar 

  25. Shevchishin V.V.: Removable singularities of codimension Three of Yang-Mills and holomorphic vector bundles. Dokl. Akad. Nauk Ukr. 1992, No. 7, 8–10 (in Russian)

    Google Scholar 

  26. Shevchishin, V.V.: The Thullen type extension theorem for holomorphic vector bundles withL 2-bounds on curvature. Ph.D. Thesis, Bochum, 1994

  27. Shiffman, B.: Extension of positive line bundles and meromorphic maps. Invent. Math.15 (1972), 332–347

    Google Scholar 

  28. Sibner, L.M., Sibner, R.J.: Singular Sobolev connections with holonomy. Bull. AMS19 (1988), 471–473

    Google Scholar 

  29. Sibner, L.M., Sibner, R.J.: Classification of singular Sobolev connections by their holonomy. Commun. Math. Phys.144 (1992), 337–350

    Google Scholar 

  30. Sibner, L.M., Sibner, R.J., Uhlenbeck, K.: Solutions to Yang-Mills equations that are not self-dual. Proc. Natl. Acad. Sci. USA86 (1989), 8610–8613

    Google Scholar 

  31. Siu, Y.-T.: Techniques of extension of analytic objects. Marcel Dekker, New York, 1974

    Google Scholar 

  32. Siu, Y.-T.: A Thullen type extension theorem for positive holomorphic vector bundles. Bull. AMS78 (1972), 775–776

    Google Scholar 

  33. Siu, Y.-T.: Extending coherent analytic sheaves Ann. of Math.90 (1969), 108–143

    Google Scholar 

  34. Smith, P.D.: Removable singularities for the Yang-Mills-Higgs equations in two dimension. Ann. Inst. Henri Poincaré, Analyse non linéaire7 (1990), 561–588

    Google Scholar 

  35. Trautmann, G.: Ein Kontinuitätssatz für die Fortsetzung kohärenter analytischer Garben. Arch. Math.18 (1967), 188–196

    Google Scholar 

  36. Uhlenbeck, K.: Connections withL p-bounds on curvature. Commun. Math. Phys.83 (1982), 31–42

    Google Scholar 

  37. Uhlenbeck, K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83 (1982), 11–29

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shevchishin, V.V. The Thullen type extension theorem for holomorphic vector bundles withL 2-bounds on curvature. Math. Ann. 305, 461–491 (1996). https://doi.org/10.1007/BF01444234

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444234

Mathematics Subject Classification (1991)

Navigation