Skip to main content
SpringerLink
Log in

Intrinsic Semiharmonic Maps

  • Published:
Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

For maps from a domain Ω⊂ℝm into a Riemannian manifold N, a functional coming from the norm of a fractional Sobolev space has recently been studied by Da Lio and Rivière. An intrinsically defined functional with a similar behavior also exists, and its first variation can be identified with a Dirichlet-to-Neumann map belonging to the harmonic map problem. The critical points have regularity properties analogous to harmonic maps.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bethuel, F.: On the singular set of stationary harmonic maps. Manuscr. Math. 78, 417–443 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Da Lio, F., Rivière, T.: 3-commutators estimates and the regularity of 1/2-harmonic maps into spheres, arXiv:0901.2533v2 [math.AP] (2009)

  3. Eells, J., Lemaire, L.: A report on harmonic maps. Bull. Lond. Math. Soc. 10, 1–68 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hélein, F.: Régularité des applications faiblement harmoniques entre une surface et une sphère. C. R. Acad. Sci. Paris Sér. I Math. 311, 519–524 (1990)

    MATH  Google Scholar 

  5. Hélein, F.: Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne. C. R. Acad. Sci. Paris Sér. I Math. 312, 591–596 (1991)

    MATH  Google Scholar 

  6. Jäger, W., Kaul, H.: Uniqueness and stability of harmonic maps and their Jacobi fields. Manuscr. Math. 28, 269–291 (1979)

    Article  MATH  Google Scholar 

  7. Jäger, W., Kaul, H.: Uniqueness of harmonic mappings and of solutions of elliptic equations on Riemannian manifolds. Math. Ann. 240, 231–250 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Moser, R.: Unique solvability of the Dirichlet problem for weakly harmonic maps. Manuscr. Math. 105, 379–399 (2001)

    Article  MATH  Google Scholar 

  9. Nash, J.: The imbedding problem for Riemannian manifolds. Ann. Math. (2) 63, 20–63 (1956)

    Article  MathSciNet  Google Scholar 

  10. Price, P.: A monotonicity formula for Yang–Mills fields. Manuscr. Math. 43, 131–166 (1983)

    Article  MATH  Google Scholar 

  11. Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math. (2) 113, 1–24 (1981)

    Article  MathSciNet  Google Scholar 

  12. Scheven, C.: Partial regularity for stationary harmonic maps at a free boundary. Math. Z. 253, 135–157 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Simon, L.: Theorems on Regularity and Singularity of Energy Minimizing Maps. Lectures in Math. ETH Zürich. Birkhäuser, Basel (1996)

    MATH  Google Scholar 

  14. Struwe, M.: Uniqueness of harmonic maps with small energy. Manuscr. Math. 96, 463–486 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

    Roger Moser

Authors
  1. Roger Moser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roger Moser.

Additional information

Communicated by Alexander Isaev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moser, R. Intrinsic Semiharmonic Maps. J Geom Anal 21, 588–598 (2011). https://doi.org/10.1007/s12220-010-9159-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12220-010-9159-7

Keywords

Mathematics Subject Classification (2000)

Search

Navigation