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Nodal sets of eigenfunctions on Reimannian manifolds

Inventiones mathematicae volume 93, pages 161–183 (1988)Cite this article

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References

  1. Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations of second order. J. Math. Pures Appl.36, 235–249 (1957)

    Google Scholar 

  2. Bishop, R., Crittenden, R.: Geometry of Manifolds. New York-London: Academic Press, 1964

    Google Scholar 

  3. Brüning, J.: Über Knoten von Eigenfunktionen des Laplace Beltrami operator. Math. Z.158, 15–21 (1978)

    Google Scholar 

  4. Cheeger, J., Gromov, M., Taylor, M.: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differ. Geom.17, 15–53 (1982)

    Google Scholar 

  5. Cheng, S. Y.: Eigenfunctions and nodal sets. Comment. Math. Helv.51, 43–55 (1976)

    Google Scholar 

  6. Cheng, S. Y., Yau, S. T.: Differential equations on Riemannian manifolds and their geometric applications. Commun. Pure Appl. Math.28, 333–354 (1975)

    Google Scholar 

  7. Federer, H.: Geometric measure, theory. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  8. Hörmander, L.: Linear partial differential operators. Berlin-Heidelberg-New York: Springer 1963

    Google Scholar 

  9. Stein, E., Weiss, G.: Fourier analysis on Euclidean spaces. Princeton: Princeton University Press 1971

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    Harold Donnelly

  2. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Charles Fefferman

Authors
  1. Harold Donnelly
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  2. Charles Fefferman
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Additional information

Supported by NSF Grant # DMS-8610730 (1)

Supported by NSF Grant $ DMS85-04342

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Donnelly, H., Fefferman, C. Nodal sets of eigenfunctions on Reimannian manifolds. Invent Math 93, 161–183 (1988). https://doi.org/10.1007/BF01393691

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  • DOI: https://doi.org/10.1007/BF01393691

Keywords

  • Manifold
  • Reimannian Manifold