References
Berger, M., Gauduchon, P., andMazet, E.,Le Spectre d'une Variété Riemannienë, Lecture Notes in Mathematics, #194 (1971), Springer-Verlag, New York.
Bombieri, E.,Theory of Minimal Surfaces and a Counterexample to the Bernstein Conjecture in High Dimensions, Lecture Notes (1970), Courant Institute, N.Y.U., New York.
Chavel, I. andFeldman, E. A.,Spectra of domains on compact manifolds, J. of Functional Anal.,30 (1978), 192–222.
Cheeger, J.,A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, A symposium in honor of S. Bochner, Princeton University Press, Princeton, N.J., (1970), 195–199.
Courant, R. andHilbert, D.,Methods of Mathematical Physics, vol. I, Interscience, New York, 1953.
Fiala, F.,Le probleme des isoperimètres sur les surfaces ouvertes a courbure positive, Comment. Math. Helv.,13 (1941), 293–346.
Kac, M.,Can you hear the shape of a drum?, Amer. Math. Monthly,73 (1966), 1–23.
Li, P.,On the Sobolev constant and the p-spectrum of a compact Riemannian manifold, preprint.
McKean, H. P.,Stochastic Integrals, Academic Press, New York.
McKean, H. P. andSinger, I. M.,Curvature and the eigenvalues of the Laplacian, J. of Diff. Geometry,1 (1967), 43–70.
Osserman, R.,Bonnerson-style isoperimetric inequalities, Amer. Math. Monthly, (1979), 1–29.
Port, S. C. andStone, C. J.,Brownian Motion and Classical Potential Theory, Academic Press, New York, 1978.
Rauch, J. andTaylor, M.,Potential and scattering theory on wildly perturbed domains, J. of Functional Anal.,18 (1975), 27–59.
Yau, S. T.,Isoperimetric constants and the first eigenvalue of a compact manifold, Ann. Sci. Ecole Norm. Sup. (4o Sci),8 (1975), 487–507.
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ToH. E. Rauch, in memoriam
Partially supported by N.S.F. Grant MCS 77-02757
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Chavel, I., Feldman, E.A. Spectra of manifolds with small handles. Commentarii Mathematici Helvetici 56, 83–102 (1981). https://doi.org/10.1007/BF02566200
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DOI: https://doi.org/10.1007/BF02566200