Related papers: $L^2$-Gamma-Fredholmness for spacetimes

We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to…

We show that the residue density of the logarithm of a generalised Laplacian on a closed manifold defines an invariant polynomial valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential…

In this work, we prove a compactness theorem on the space of all Hamiltonian stationay Lagrangian submanifolds in a compact symplectic manifold with uniform bounds on area and total extrinsic curvature.

Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an $L_\infty$ algebra attached to the foliation de-Rham complex…

Under two boundary conditions, the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized -Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on…

In this paper, the Cauchy problem for a Friedrichs system on a globally hyperbolic manifold with a timelike boundary is investigated. By imposing admissible boundary conditions, the existence and the uniqueness of strong solutions are…

The paper concerns the general linear one-dimensional second-order hyperbolic equation $$ \partial^2_tu - a^2(x,t)\partial^2_xu + a_1(x,t)\partial_tu + a_2(x,t)\partial_xu + a_3(x,t)u=f(x,t), \quad x\in(0,1) $$ with periodic conditions in…

We show that for a smooth closed curve $\gamma$ on a compact Riemannian surface without boundary, the inner product of two eigenfunctions $e_\lambda$ and $e_\mu$ restricted to $\gamma$, $|\int e_\lambda\overline{e_\mu}\,ds|$, is bounded by…

We study various topological invariants on a torsional geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH = 0, which appears in string theory compactification scenarios. By using the identification…

Let $X=G/H$ be a homogeneous space, where $G \supset H$ are reductive Lie groups. We ask: in the setting where $\Gamma \backslash G/H$ is a standard quotient, to what extent can the discrete subgroup $\Gamma$ be deformed while preserving…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…

This paper presents the Fredholm theory on l^p-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p=\infty…

We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the…

Let $(M,g)$ be a compact Riemannian surface with nonpositive sectional curvature and let $\gamma$ be a closed geodesic in $M$. And let $e_\lambda$ be an $L^2$-normalized eigenfunction of the Laplace-Beltrami operator $\Delta_g$ with…

We consider the massive Klein-Gordon equation on short-range asymptotically Minkowski spacetimes. Extending our results in [GW1], we show that the Klein-Gordon operator with Feynman type boundary conditions at infinite times is invertible…

We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip $[0,1]\times\R$. We state rather broad natural conditions on the data under which the operators of…

We present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by…

We develop a Fredholm Theory for the Hodge Laplacian in weighted spaces on ALG$^*$ manifolds in dimension four. We then give several applications of this theory. First, we show the existence of harmonic functions with prescribed asymptotics…

In this paper we describe the behavior of solutions of the Klein-Gordon equation, (Box_g+lambda)u=f, on Lorentzian manifolds (X^o,g) which are anti-de Sitter-like (AdS-like) at infinity. Such manifolds are Lorentzian analogues of the…

We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is…