相关论文: Local obstructions to a conformally invariant equa…
We introduce new `refined' obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate--Shafarevich groups, we show that the Hasse principle and weak approximation for…
In this article we construct a complete system of M\"obius-geometric invariants for pairs $(S^m, S^l), l \leq m$, of spheres contained in the M\"obius space $S^n$. It consists of n-m generalised stationary angles. We interpret these…
We introduce two basic invariant forms which define generic surface in 3-space uniquely up to Lie sphere equivalence. Two particularly interesting classes of surfaces associated with these invariants are considered, namely, the Lie-minimal…
We study certain obstacle type problems involving standard and nonlocal minimal surfaces. We obtain optimal regularity of the solution and a characterization of the free boundary.
We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic…
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majority of the cases when this group is non-zero. Our approach is…
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on div-conforming Raviart-Thomas boundary elements…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.
We investigate obstruction classes of moduli spaces of sheaves on K3 surfaces. We extend previous results by Caldararu, explicitly determining the obstruction class and its order in the Brauer group. Our main theorem establishes a short…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
In this article we give general neccessary and sufficient conditions to ensure that a pseudo-Riemannian manifold is conformal to an Einstein space. These conditions are algorithmic in \emph{the metric tensor} whenever the Weyl endomorphism…
A Pfaff field on a projective space is a map from the sheaf of differential s-forms, for a certain s, to an invertible sheaf. The interesting ones are those arising from a Pfaff system, as they give rise to a distribution away from their…
We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…
The Seiberg-Witten equation with multiple spinors generalises the classical Seiberg-Witten equation in dimension three. In contrast to the classical case, the moduli space of solutions $\mathcal{M}$ can be non-compact due to the appearance…
The paper provides computations of the first non-vanishing $\mathbb{A}^1$-homotopy sheaves of the orthogonal Stiefel varieties which are relevant for the unstable isometry classification of quadratic forms over smooth affine schemes over…
In [LP] the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p_g>0 are a sum of such local GW invariants. This paper describes how the local…
In this paper, we compute the open Gromov-Witten invariants for every compact toric surface X which is semi-Fano (i.e. the anticanonical line bundle is nef). Unlike the Fano case, this involves non-trivial obstructions in the corresponding…
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…
In this paper we study a singularly modified version of the incompressible porous media equation. We investigate the implications for the local well-posedness of the equations by modifying, with a fractional derivative, the constitutive…