相关论文: On Imprisoned Curves and b-length in General Relat…

We study local variations of causal curves in a space-time with respect to b-length (or generalised affine parameter length). In a convex normal neighbourhood, causal curves of maximal metric length are geodesics. Using variational…

We prove that every open connected region of relativistic spacetime $(M,\textbf{g})$ that encloses a $b$-incomplete half-curve has an open connected subregion that encloses a $b$-incomplete half-curve and is also 'small' in the following…

The b-boundary construction by B. Schmidt is a general way of providing a boundary to a manifold with connection. It has been shown to have undesirable topological properties however. C. J. S. Clarke gave a result showing that for…

One of the known mathematical descriptions of singularities in General Relativity is the b-boundary, which is a way of attaching endpoints to inextendible endless curves in a spacetime. The b-boundary of a manifold M with connection is…

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…

Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in my earlier paper. This paper proposes a closure operation on internal preneighbourhood…

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of…

Here we extend the notion of target-local Gromov convergence of pseudoholomorphic curves to the case in which the target manifold is not compact, but rather is exhausted by compact neighborhoods. Under the assumption that the curves in…

For a class of compactly supported windows we characterize the frame property for a Gabor system $\mts,$ for translation parameters $a$ belonging to a certain range depending on the support size. We show that the obstructions to the frame…

In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…

In this paper we prove that the unit ball $\mathbb{B}$ of $\mathbb{C}^2$ admits complete properly embedded complex curves of any given topological type. Moreover, we provide examples containing any given closed discrete subset of…

We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…

The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proved that feeble distinction, a property which stays between weak…

We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de-Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For…

We consider pairs (X,Y) where X is a compact, locally CAT(-1) space, and Y is a totally geodesic subspace. The inclusion induces an embedding of the boundaries at infinity of the universal covers; we focus on the case where these are…

Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian submersions with totally geodesic fibers. In particular, we…

It is a result of Gruson and Peskine that the invariants of a set points in $\ptwo$ in general position are connected. Associated to a space curve there are sequences of invariants which generalize the invariants of points in $\ptwo$. The…

In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of $C^2$) polynomials whose Newton polygon is either a triangle or a line segment. Our classification has several…