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A non-existence theorem for pluriharmonic maps of finite energy

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References

  1. Demailly, J.P.: EstimationsL 2 pour l'opérateur\(\bar \partial\) d'un fibré vectoriel holomorphr semi-positif au-dessus d'une variété Kahlérienne complete. Ann. Sci. Éc. Norm. Super.15, 457–511 (1982)

    Google Scholar 

  2. Eells, J., Lemaire, L.: Selected topics in harmonic maps. Providence, A.M.S. 1983

    Google Scholar 

  3. Eells, J., Sampsom, J.H.: Harmonic mappings of Riemannian manifolds. Am. J. Math.86, 109–160 (1964)

    Google Scholar 

  4. Greene, R.E., Wu, H.: Curvature and complex analysis. Bull. Am. Math. Soc.77, 1045–1049 (1971)

    Google Scholar 

  5. Greene, R.E., Wu, H.: Integrals of subharmonic functions on manifolds of non-negative curvature. Invent. Math.27, 265–298 (1974)

    Google Scholar 

  6. Greene, R.E., Wu, H.:C ∞ convex functions and manifolds of positive curvature. Acta Math.137, 209–245 (1976)

    Google Scholar 

  7. Greene, R.E., Wu, H.: On Kähler manifolds of positive bisectional curvature and a theorem of Hartogs. Abh. Math. Sem. Univ. Humburg.47, 171–185 (1978)

    Google Scholar 

  8. Karp, L.: On Stokes' theorem for noncompact manifolds. Proc. Am. Math. Soc.82, 487–490 (1981)

    Google Scholar 

  9. Ohsawa, T.: A reduction theorem of cohomology groups of very stronglyq-convex Kähler manifolds. Invent. Math.63, 335–354 (1981)

    Google Scholar 

  10. Sampson, J.H.: Some properties and applications of harmonic mappings. Ann. Sci. Ec. Norm. Super.11, 211–228 (1978)

    Google Scholar 

  11. Sampson, J.H.: On harmonic mappings. Symp. Math.26, 197–210 (1982)

    Google Scholar 

  12. Schneider, M.: Über eine Vermutung von Hartshorne. Math. Ann.201, 221–229 (1973)

    Google Scholar 

  13. Schneider, M.: Lefschetz theorems and a vanishing theorem of Grauert-Riemenschneider. Proc. of Symp. in Pure Math.30, 35–39 (1977)

    Google Scholar 

  14. Schoen, R., Yau, S.T.: Harmonic maps and the topology of stable hypersurfaces and manifolds of non-negative Ricci curvature. Comm. Math. Helv.51, 333–341 (1976)

    Google Scholar 

  15. Sealey, H.C.J.: Some conditions ensuring the vanishing of harmonic differential forms with applications to harmonic maps and Yang-Mills theory. Math. Proc. Camb. Phil. Soc.91, 441–452 (1982)

    Google Scholar 

  16. Siu, Y.T.: Complex analyticity of harmonic maps, vanishing and Lefschetz theorems. J. Differ. Geom.17, 55–138 (1982)

    Google Scholar 

  17. Takegoshi, K.:L 2 cohomology of Kähler metrics of Bergman type. Preprint

  18. Yau, S.T.: Harmonic functions on complete Riemannian manifolds. Commun. Pure Appl. Math.28, 201–228 (1975)

    Google Scholar 

  19. Yau, S.T.: Some function theoretic properties of complete Riemannian manifolds and their applications to geometry. Indiana J. Math.25, 659–670 (1976)

    Google Scholar 

  20. Yau, S.T.: A general Schwarz lemma for Kähler manifolds, Am. J. Math.100, 197–203 (1978)

    Google Scholar 

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  1. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Kensho Takegoshi

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  1. Kensho Takegoshi
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Takegoshi, K. A non-existence theorem for pluriharmonic maps of finite energy. Math Z 192, 21–27 (1986). https://doi.org/10.1007/BF01162016

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