Dodziuk, Jozef Eigenvalues of the Laplacian on forms. (English) Zbl 0502.58038 Proc. Am. Math. Soc. 85, 437-443 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 33 Documents MSC: 58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 53C20 Global Riemannian geometry, including pinching Keywords:Laplacian on forms; geometric estimates for eigenvalues of the Laplacian; first eigenvalue of the Laplacian; Rayleigh-Ritz quotient; injectivity radius Citations:Zbl 0329.53035 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Richard L. Bishop and Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. · Zbl 0984.53001 [2] Shiu Yuen Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), no. 3, 289 – 297. · Zbl 0329.53035 · doi:10.1007/BF01214381 [3] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. · Zbl 0051.28802 [4] J. Eichhorn, Das Spektrum von \( {\Delta _p}\) auf offenen Riemannschen Mannigfaltigkeiten mit beschränkter Schmitt-krümmung und beschranktem Kern-Tensor, preprint. [5] Stéfan Hildebrandt, Helmut Kaul, and Kjell-Ove Widman, An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math. 138 (1977), no. 1-2, 1 – 16. · Zbl 0356.53015 · doi:10.1007/BF02392311 [6] M. Gromov, Paul Lévy’s isoperimetric inequality, preprint. [7] Helmut Kaul, Schranken für die Christoffelsymbole, Manuscripta Math. 19 (1976), no. 3, 261 – 273. · Zbl 0332.53025 · doi:10.1007/BF01170775 [8] Jürgen Kern, Das Pinchingproblem in Fastriemannschen Finslerschen Mannigfaltigkeiten, Manuscripta Math. 4 (1971), 341 – 350 (German, with English summary). · Zbl 0211.24801 · doi:10.1007/BF01168701 [9] D. B. Ray and I. M. Singer, \?-torsion and the Laplacian on Riemannian manifolds, Advances in Math. 7 (1971), 145 – 210. · Zbl 0239.58014 · doi:10.1016/0001-8708(71)90045-4 [10] G. de Rham, Variétés différentiables, Hermann, Paris, 1955. · Zbl 0065.32401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.