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.
Eigenvalue and gap estimates for the Laplacian acting on p-forms / P., Guerini; Savo, Alessandro. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 356:1(2004), pp. 319-344. [10.1090/s0002-9947-03-03336-1]
Eigenvalue and gap estimates for the Laplacian acting on p-forms
SAVO, Alessandro
2004
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
