Acta Mathematica

Every covering of a compact Riemann surface of genus greater than one carries a nontrivial L2 harmonic differential

Jozef Dodziuk

Full-text: Open access


Research supported in part by the National Science Foundation Grant No. MCS8024276 and by the Sloan Fellowship.

Article information

Acta Math. Volume 152 (1984), 49-56.

Received: 22 November 1982
First available in Project Euclid: 31 January 2017

Permanent link to this document

Digital Object Identifier

Zentralblatt MATH identifier

1984 © Almqvist & Wiksell


Dodziuk, Jozef. Every covering of a compact Riemann surface of genus greater than one carries a nontrivial L 2 harmonic differential. Acta Math. 152 (1984), 49--56. doi:10.1007/BF02392190.

Export citation


  • Ahlfors, L. V., Zur Theorie der Überlagerungsflächen. Acta Math., 65 (1935), 157–194.
  • —, Open Riemann surfaces and extremal on compact subregions. Comment. Math. Helv., 24 (1950), 100–134.
  • Ahlfors, L. V. & Sario, L., Riemann Surfaces. Princeton University Press, Princeton, 1960.
  • Atiyah, M. F., Elliptic operators, discrete groups and von Neumann algebras. Astérisque, 32, 33 (1976), 43–72.
  • Azencott, R., Behavior of diffusion semi-groups at infinity. Bull. Soc. Math. France, 102 (1974), 193–240.
  • Cheeger, J., On the Hodge theory of Riemannian pseudomanifolds, in Geometry of the Laplace operator. Proc. Symp. Pure Math., vol. 36, Amer. Math. Soc., Providence 1980, 91–146.
  • —, A lower bound for the smallest eigenvalue of the Laplacian, in Problems in analysis, a symposium in honor of S. Bochner. Princeton University Press, Princeton 1970, 195–199.
  • DeBaun, D., L2-cohomology of noncompact surfaces. Ph.D. Thesis, University of Pennsylvania 1980.
  • Fischer-Colbrie, D. & Schoen, R., The structure of complete stable minimal surfaces in 3-manifolds of nonegative scalar curvature. Comm. Pure Appl. Math., 33 (1980), 199–211.
  • Kra, I., Automorphic forms and Kleinian groups, W. A. Benjamin, Reading 1972.
  • Maskit, B., The conformal groups of a plane domain. Amer. J. Math., 90 (1968), 718–722.
  • Myrberg, P. J., Die Kapazität der Singulären Menge der Linearen Gruppen. Ann. Acad. Sci. Fenn. Ser. A.I., 10 (1941).
  • Nishino, T., Prolongements analytiques au sense de Riemann. Bull. Soc. Math. France, 107 (1979), 97–112.
  • Prat, J. J., Étude asymptotique du movement brownien sur une variété riemannienne à courbure négative. C.R. Acad. Sci. Paris, 272 (1971), 1586–1589.
  • DeRham, G., Variétés Différentiables. Hermann, Paris 1973.
  • Seidel, W., On a metric property of Fuchsian groups. Proc. Nat. Acad. Sci., 21 (1935), 475–478.
  • Sinai, Ya. G., Measures invariantes des Y-systemes. Actes Congress Intern. Mathem., Paris 1970, vol. 2, 920–940.
  • Sullivan, D., λ-Potential theory on manifolds. Preprint.
  • Vauthier, J., Diffusion sur une variété riemannienne complète à courbure négative. C. R. Acad. Sci. Paris, 275 (1972), 925–926.