相关论文: A remark on differentiability of Cauchy horizons

The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.

We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott-Chern cohomology in terms of Betti…

We prove a comparison isomorphism between singular cohomology and sheaf cohomology.

We prove a linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow. We then use this sharp differential inequality to study the Liouville properties of the plurisubharmonic functions on complete Kaehler manifolds with nonnegative…

We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a…

We study the obstructions to coarse universality in separable dual Banach spaces. We prove coarse non-universality of several classes of dual spaces, including those with conditional spreading bases, as well as generalized James and James…

In this article we use techniques developed by Hrushovski-Loeser to study certain metric properties of the Berkovich analytification of a finite morphism of smooth connected projective curves. In recent work, M. Temkin proved a radiality…

In this paper, we give a new proof of the foundational result, due to S. Cutkosky, on the existence of a monomialisation of a morphism from a 3-fold to a surface. Our proof brings to the fore the notion of log-Fitting ideals, and requires…

We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke's point, Kariya's point, and to other remarkable points from the triangle geometry.

Apparent horizons are structures of spacelike hypersurfaces that can be determined locally in time. Closed surfaces of constant expansion (CE surfaces) are a generalisation of apparent horizons. I present an efficient method for locating CE…

We prove a number of basic vanishing results for modified diagonal classes. We also obtain some sharp results for modified diagonals of curves and abelian varieties, and we prove a conjecture of O'Grady about modified diagonals on double…

In this work we prove that, for a general polyhedral domain of $\mathbb{R}^3$, the cohomology spaces of the discrete de Rham complex of [Di Pietro and Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness,…

This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble…

We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous…

We investigate several closely related "homothety conjectures" for convex bodies on a plane. Using the modern language of differential geometry, we systematically derive the fundamental properties of bodies of flotation, bodies of buoyancy,…

As is well known, constant mean curvature (CMC) spacelike hypersurfaces play an important role in solving the Einstein equations, both in solving the contraints and the evolution equations. In this paper we review the CMC existence result…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was…