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

Guerini, P; Savo, A (2004). Eigenvalue and gap estimates for the Laplacian acting on p-forms. Transactions of the American Mathematical Society, 356(1):319-344 (electronic).

Abstract

We study the gap of the ﬁrst eigenvalue of the Hodge Laplacian acting on p-diﬀerential forms of a manifold with boundary, for consecutive values of the degree p.
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.

Abstract

We study the gap of the ﬁrst eigenvalue of the Hodge Laplacian acting on p-diﬀerential forms of a manifold with boundary, for consecutive values of the degree p.
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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Citations

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