相关论文: Subelliptic Spin_C Dirac operators, I

In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We…

In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the…

Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. Limiting cases are characterized by the existence of…

We study the $\eta$-invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the help of heat kernel methods. In even dimensions, we relate this invariant to $\eta$-invariants of a boundary Dirac…

In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gau{\ss}-Bonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds these operators in general do not have…

The aim of this paper is to study a possible "boundary phenomenon" for Spinc Dirac operators in a special case. If you parametrise Spinc Dirac operators by a family of connections on a Spinc 4-manifold with boundary, this boundary inherits…

We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary…

In [10], Dabrowski etc. gave spectral Einstein bilinear functionals of differential forms for the Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski…

We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we…

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with…

We study a Dirac operator subject to Atiayh-Patodi-Singer like boundary conditions on the solid torus and show that the corresponding boundary value problem is elliptic, in the sense that the Dirac operator has a compact parametrix.

We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while…

Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional…

We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in…

In this article, we prove a Sobolev-like inequality for the Dirac operator on closed compact Riemannian spin manifolds with a nearly optimal Sobolev constant. As an application, we give a criterion for the existence of solutions to a…

We use the Dirac operator technique to establish sharp distance estimates for compact spin manifolds under lower bounds on the scalar curvature in the interior and on the mean curvature of the boundary. In the situations we consider, we…

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…

We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a "geometric Witt condition". We accomplish this by cutting off to a smooth manifold with boundary, applying the…

We study strictly elliptic differential operators with Dirichlet boundary conditions on the space $\mathrm{C}(\overline{M})$ of continuous functions on a compact, Riemannian manifold $\overline{M}$ with boundary and prove sectoriality with…