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Displaying similar documents to “The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry.”

Boundary value problems and layer potentials on manifolds with cylindrical ends

Marius Mitrea, Victor Nistor (2007)

Czechoslovak Mathematical Journal

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We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators...

Comparison of Dirac operators on manifolds with

Bunke, Ulrich

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The author introduces boundary conditions for Dirac operators D giving selfadjoint extensions such that the Hamiltonians H = D 2 define elliptic operators. Using finite propagation speed methods and assuming bounded geometry he estimates the trace of the difference of two heat operators e - t H associated to a pair of Dirac operators coinciding on cocompact sets.

Geometric heat kernel coefficient for APS-type boundary conditions

Gorm Salomonsen (1998)

Journées équations aux dérivées partielles

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I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.