Related papers: A Kobayashi pseudo-distance for holomorphic bracke…

We prove that for a pseudoconvex domain of the form $\mathfrak{A} = \{(z, w) \in \mathbb C^2 : v > F(z, u)\}$, where $w = u + iv$ and F is a continuous function on ${\mathbb C}_z \times {\mathbb R}_u$, the following conditions are…

Supersymmetric bosonic backgrounds governed by first-order BPS equations, can be realised in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting…

By introducing the notion of distributive constant for a family of closed subschemes, we establish a general form of the second main theorem for algebraic nondegenerate meromorphic mappings from a generalized $p$-Parabolic manifold into a…

Let $D=\{\rho < 0\}$ be a smooth relatively compact domain in an almost complex manifold $(M,J)$, where $\rho$ is a smooth defining function of $D$, strictly $J$-plurisubharmonic in a neighborhood of the closure $\overline{D}$ of $D$. We…

This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in $\mathbb{P}^3$ of degree at least $17$ is Kobayashi hyperbolic. -- The complement of a {\em generic}…

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…

This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…

We present a geometric approach to defining an algebra $\hat{\mathcal G}(M)$ (the Colombeau algebra) of generalized functions on a smooth manifold $M$ containing the space ${\mathcal D}'(M)$ of distributions on $M$. Based on differential…

Duke, Imamo\=glu, and T\'oth have recently constructed a new geometric invariant, a hyperbolic orbifold, associated to each narrow ideal class of a real quadratic field. Furthermore, they have shown that the projection of these hyperbolic…

By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…

Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are…

Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to…

We discuss two generalizations of the collar lemma. The first is the stable neighborhood theorem which says that a (not necessarily simple) closed geodesic in a hyperbolic surface has a \lq\lq stable neighborhood\rq\rq whose width only…

We classify the polycyclic totally ordered simple dimension groups, i.e. dimension groups given by a dense embedding of n-dimensional lattice into the real line. Our method is based on the geometry of simple geodesics on the hyperbolic…

We provide a general sufficient condition for extendability of quasimorphisms on subgroups. This condition recovers the result of Hull--Osin on quasimorphisms on hyperbolically embedded subgroups, and the proof given in this paper is much…

It is well known that the category of real Lie supergroups is equivalent to the category of the so-called (real) Harish-Chandra pairs. That means that a Lie supergroup depends only on the underlying Lie group and its Lie superalgebra with…

In this paper we give a characterization in terms of ``quasi-geodesics frames' of visibility and existence of geodesic loops for bounded domains in $\mathbb C^d$ which are Kobayashi complete hyperbolic and Gromov hyperbolic.

We describe a family of smooth contractible algebraic surfaces $X$ different from $\C^2$ such that $X$ admits dominant holomorphic maps from $\C^2$ and there is a unique line $E$ in $X$ for which the Kobayashi-Royden pseudometric vanishes…

In this paper, we obtain the Gehring-Hayman type theorem on smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As an application, we provide a quantitative comparison between global and local Kobayashi distances near a…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…