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Nodal sets for eigenfunctions of the Laplacian on surfaces
Author(s):
Harold
Donnelly;
Charles
Fefferman
Journal:
J. Amer. Math. Soc.
3
(1990),
333-353.
MSC:
Primary 58G25;
Secondary 35P05
MathSciNet review:
1035413
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References:
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- N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations of second order, J. Math. Pures Appl. 36 (1957), 235-249. MR 0092067 (19:1056c)
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- T. Carleman, Sur les systémes linéares aux dérivées partielles du premier ordre á deux variables, C. R. Acad. Sci. Paris Ser. I Math. 197 (1933), 471-474.
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- J. Cheeger, Finiteness theorems in Riemannian geometry, Amer. J. Math. 92 (1970), 61-74. MR 0263092 (41:7697)
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- -, Nodal sets of eigenfunctions: Riemannian manifolds with boundary, Moser volume, Analysis, Academic Press, New York, 1990, pp. 251-262. MR 1039348 (92e:58216)
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- S. Goldberg, Curvature and homology, Dover, New York, 1962. MR 0139098 (25:2537)
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- R. S. Hardt and L. Simon, Nodal sets of solutions of elliptic equations, J. Differential Geom. 30 (1989), 505-522. MR 1010169 (90m:58031)
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- J. Jost, Harmonic maps between surfaces, Lecture Notes in Math., vol 1062, Springer-Verlag, Berlin, Heidelberg, and New York, 1984. MR 754769 (85j:58046)
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- N. S. Nadirashvili, Length of nodal sets of eigenfunctions of the Laplace operator, Uspekhi Mat. Nauk 43 (1988), 219-220. MR 969585 (90e:58161)
- [11]
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
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Additional Information:
DOI:
10.1090/S0894-0347-1990-1035413-2
PII:
S0894-0347-1990-1035413-2
Copyright of article:
Copyright
1990,
American Mathematical Society
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