Eigenvalue and gap estimates for the Laplacian acting on  -forms |
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| Authors: | Pierre Guerini Alessandro Savo |
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| Affiliation: | Institut für Mathematik, Universität Zürich Irchel, Winterthurerstrasse 90, CH-8057 Zürich, Switzerland ; Dipartimento di Metodi e Modelli Matematici, Università di Roma I La Sapienza, Via Antonio Scarpa 16, 00161 Roma, Italy |
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| Abstract: | We study the gap of the first eigenvalue of the Hodge Laplacian acting on  -differential forms of a manifold with boundary, for consecutive values of the degree  . We first show that the gap may assume any sign. Then we give sufficient conditions on the intrinsic and extrinsic geometry to control it. Finally, we estimate the first Hodge eigenvalue of manifolds whose boundaries have some degree of convexity. |
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| Keywords: | Hodge Laplacian eigenvalues gaps convex manifolds |
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