Skip to main content
Log in

Heat Flows of Subelliptic Harmonic Maps into Riemannian Manifolds with Nonpositive Curvatures

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

Abstract

In this paper, we discuss the heat flows of subelliptic harmonic maps into Riemannian manifolds with nonpositive curvatures, and prove the homotopic existence which is a generalization of the Eells–Sampson theorem.

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.

Similar content being viewed by others

References

  1. Ding, W.Y.: Lectures on Heat Flow of Harmonic Maps. Preprint

  2. Eells, J., Sampson, J.: Harmonic mappings of Riemannian manifolds. Am. J. Math. 85, 109–160 (1964)

    Article  MathSciNet  Google Scholar 

  3. Hajlasz, P., Strzelecki, P.: Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces. Math. Ann. 312, 341–362 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jost, J.: Riemannian Geometry and Geometric Analysis, 3rd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  5. Jost, J., Xu, C.J.: Subelliptic harmonic maps. Trans. Am. Math. Soc. 350(11), 4633–4649 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jost, J., Yang, Y.-H.: Heat flow for horizontal harmonic maps into a class of Carnot–Carathéodory spaces. arXiv:math/0312144v1 [math.DG], 7 Dec. (2003)

  7. Sanchez-Calle, A.: Fundamental solutions and geometry of the sum of squares of vector fields. Invent. Math. 78, 142–160 (1984)

    Article  MathSciNet  Google Scholar 

  8. Strichartz, R.S.: Sub-Riemannian geometry. J. Differ. Geom. 24, 221–263 (1986)

    MathSciNet  MATH  Google Scholar 

  9. Wang, C.: Subelliptic harmonic maps from Carnot groups. Calc. Var. 18, 95–115 (2003)

    Article  MATH  Google Scholar 

  10. Zhou, Z.R.: Uniqueness of subelliptic harmonic maps. Ann. Glob. Anal. Geom. 17(6), 581–594 (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhen-Rong Zhou.

Additional information

Communicated by Jiaping Wang.

Research supported by National Science Foundation of China No. 10871149.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, ZR. Heat Flows of Subelliptic Harmonic Maps into Riemannian Manifolds with Nonpositive Curvatures. J Geom Anal 23, 471–489 (2013). https://doi.org/10.1007/s12220-011-9220-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12220-011-9220-1

Keywords

Mathematics Subject Classification (2000)

Navigation