Related papers: On twisted microdifferential modules I. Non-existe…
In this paper, we determine all simple restricted modules over the mirror Heisenberg-Virasoro algebra ${\mathfrak{D}}$, and the twisted Heisenberg-Virasoro algebra $\bar\mathfrak{D}$ with nonzero level. As applications, we characterize…
We prove solenoidal injectivity for the geodesic X-ray transform of tensor fields on simple Riemannian manifolds with $C^{1,1}$ metrics and non-positive sectional curvature. The proof of the result rests on Pestov energy estimates for a…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We prove that smooth, projective, $K$-trivial, weakly ordinary varieties over a perfect field of characteristic $p>0$ are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our…
Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S.…
Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ norms of a cascade of…
The transverse-traceless gauge condition is an important concept in the theory of gravitational wave. It is well known that vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge. Although it is…
We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the…
For a generic degree d smooth map f: N^n -> M^n we introduce its "transverse fundamental group" \pi(f), which reduces to \pi_1(M) in the case where f is a covering, and in general admits a monodromy homomorphism \pi(f) -> S_{|d|};…
By proving the existence of non-monotone and non-oscillating wavefronts for the Nicholson's blowflies diffusive equation (the NDE), we answer an open question raised in [16]. Surprisingly, these wavefronts can be observed only for…
In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
We show there exist no nontrivial semidualizing modules for nonmodular rings of invariants of order $p^n$ with $p$ a prime.
In any dimension at least five we construct examples of closed smooth manifolds with the following properties: 1) they have neither real projective nor flat conformal structures; 2) their fundamental group is a non-elementary Gromov…
We prove a theorem on the extension of holomorphic sections of powers of adjoint bundles from submanifolds of complex codimension 1 having non-trivial normal bundle. The first such result, due to Takayama, considers the case where the…
The inner structure of the {\gamma}{\epsilon}-formalisms of Infeld and van der Waerden admits the occurrence of spin-tensor electromagnetic fields which bear invariance under the action of the generalized Weyl gauge group. A concise…
The aim of this article is to present an elementary proof of a global existence result for nonlinear wave equations satifying the null condition in an exterior domain. The novelty of our proof is to avoid completely the scaling operator…
We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…
We extend the Bondi formalism to describe asymptotically-flat spacetimes where the outgoing null geodesic congruence is not hypersurface-orthogonal, i.e. has non-vanishing twist. In the Newman-Penrose formulation, the twist…
We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be hermitian Yang-Mills, and also…