Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary
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Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary
The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.
Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable
Author: Kazuyoshi Kiyohara
language: en
Publisher: American Mathematical Soc.
Release Date: 1997
Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
Nonlinear Eigenvalues and Analytic-Hypoellipticity
Author: Ching-Chau Yu
language: en
Publisher: American Mathematical Soc.
Release Date: 1998
Explores the failure of analytic-hypoellipticity of two partial differential operators. The operators are sums of squares of real analytic vector fields and satisfy Hormander's condition. By reducing to an ordinary differential operator, the author shows the existence of non-linear eigenvalues, which is used to disprove analytic- hypoellipticity of the original operators. No index. Annotation copyrighted by Book News, Inc., Portland, OR