Eigenvalue and gap estimates for the Laplacian acting on 𝑝-forms

Guerini, Pierre; Savo, Alessandro

doi:10.1090/S0002-9947-03-03336-1

Eigenvalue and gap estimates for the Laplacian acting on -forms

Authors: Pierre Guerini and Alessandro Savo
Journal: Trans. Amer. Math. Soc. 356 (2004), 319-344
MSC (2000): Primary 58J50; Secondary 58J32
DOI: https://doi.org/10.1090/S0002-9947-03-03336-1
Published electronically: August 25, 2003
MathSciNet review: 2020035
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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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