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A spectral estimate for the Dirac operator on Riemannian flows

100%
Ginoux N., Habib G.
Open Mathematics
|
2010
|
tom 8
|
nr 5
950-965
EN
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.
2
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A lower bound for the error term in Weyl’s law for certain Heisenberg manifolds, II

100%
Nowak W.
Open Mathematics
|
2009
|
tom 7
|
nr 3
452-462
EN
This article is concerned with estimations from below for the remainder term in Weyl’s law for the spectral counting function of certain rational (2ℓ + 1)-dimensional Heisenberg manifolds. Concentrating on the case of odd ℓ, it continues the work done in part I [21] which dealt with even ℓ.
3
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Conformal Geometry and the Composite Membrane Problem

100%
Chanillo S.
Analysis and Geometry in Metric Spaces
|
2013
|
tom 1
31-35
EN
We show that a certain eigenvalue minimization problem in two dimensions for the Laplace operator in conformal classes is equivalent to the composite membrane problem. We again establish such a link in higher dimensions for eigenvalue problems stemming from the critical GJMS operators. New free boundary problems of unstable type arise in higher dimensions linked to the critical GJMS operator. In dimension four, the critical GJMS operator is exactly the Paneitz operator.
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