Related papers: The Lorentzian Calder\'{o}n problem on vector bund…

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected…

We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential collection with application to the Transformer and its token space. Our methods are catered to the…

The paper is devoted to metric connections with parallel skew-symmetric torsion in Lorentzian signature. This is motivated by recent progress in the Riemannian signature and by possible applications to supergravity theories. We provide a…

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which…

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a…

We show that there is generically non-uniqueness for the anisotropic Calder\'on problem at fixed frequency when the Dirichlet and Neumann data are measured on disjoint sets of the boundary of a given domain. More precisely, we first show…

We establish $L^2$ extension theorems for $\bar \partial$-closed $(0,q)$-forms with values in a holomorphic line bundle with smooth Hermitian metric, from a smooth hypersurface on a Stein manifold. Our result extends (and gives a new,…

Karen Uhlenbeck's compactness theorem for sequences of connections with L2 bounds on curvature applies only to connections on principal bundles with compact structure group. This article states and proves an extension of Uhlenbecks theorem…

The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this connection (which arose in Quantum Field…

On smooth manifolds of dimension $n \ge 4$, we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that…

For Maxwell's equations in a wave guide, we prove the global uniqueness in determination of the conductivity, the permeability and the permittivity by partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

We deal with Calder\'on's problem in a layered anisotropic medium $\Omega\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $\sigma=\gamma A$, where $A$ is a known Lipschitz matrix-valued function. We assume that the…

We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain…

In this article, we study the anisotropic Calder\'on problems for the non local logarithimic Schr\"odinger operators $(-\Delta_g+m)\log{(-\Delta_g+m)}+V$ with $m>1$ on a closed, connected, smooth Riemannian manifold of dimension $n\geq2$.…

Given a function $f : A \to \mathbb{R}^n$ of a certain regularity defined on some open subset $A \subseteq \mathbb{R}^m$, it is a classical problem of analysis to investigate whether the function can be extended to all of $\mathbb{R}^m$ in…

We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use…

We outline an approach to the inverse problem of Calder\'on that highlights the role of microlocal normal forms and propagation of singularities and extends a number of earlier results also in the anisotropic case. The main result states…

A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows.…

Representing vector fields by potentials can be a challenging task in domains with cavities or tunnels, due to the presence of harmonic fields which are both irrotational and solenoidal but may have no scalar or vector potentials. For…

We extend the well-known formula for the Euler class of a real oriented even-dimensional vector bundle in terms of the curvature of a metric connection to the case of a general linear connection provided a metric is present. We rewrite the…