相关论文: Nullity distributions on real hypersurfaces in non…

Let (M,p) be a smooth non-Leviflat CR hypersurface germ in complex Euclidean space of dimension 2 where p is of infinite type. The purpose of this article is to investigate the holomorphic vector fields tangent to (M,p) vanishing at p.

We present in this article a survey of recent results in value distribution theory for the Gauss maps of several classes of immersed surfaces in space forms, for example, minimal surfaces in Euclidean $n$-space ($n$=3 or 4), improper affine…

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for…

We uncover an infinite number of vacua in two-dimensional quantum field theory, the Klein-Gordon field for simplicity, by conceiving a new mode that is classified by a real positive parameter $\kappa$. We show each mode has a distinct…

We introduce an alternative definition of the relative height h^\kappa(x) of a one-dimensional fluctuating interface indexed by a continuously varying real paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to the…

The aim of this fisrt part is to introduce, for a rather large class of hypersurface singularities with 1 dimensionnal locus, the analog of the Brieskorn lattice at the origin (the singular point of the singular locus). The main results are…

We study the propagation of quantum fields on $\kappa$-Minkowsi spacetime. Starting from the non-commutative partition function for a free field written in momentum space we derive the Feynman propagator and analyze the non-trivial…

We study which $\kappa$-distributive forcing notions of size $\kappa$ can be embedded into tree Prikry forcing notions with $\kappa$-complete ultrafilters under various large cardinal assumptions. An alternative formulation -- can the…

The notion of $L^p$-distributions is introduced on Riemannian symmetric spaces of noncompact type and their main properties are established. We use a geometric description for the topology of the space of test functions in terms of the…

We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(\kappa, \mu)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we…

Local conditions on boundaries of $C^\infty$ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the…

We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the…

The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One…

In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main tools we…

Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an…

Tashiro and Tachibana proved that there exist no totally umbilical hypersurfaces in complex space forms with nonzero constant holomorphic sectional curvature, and it is also known that the shape operator of such hypersurfaces cannot be…

We consider a gravitational theory of a scalar field $\phi$ with nonminimal derivative coupling to curvature. The coupling terms have the form $\kappa_1 R\phi_{,\mu}\phi^{,\mu}$ and $\kappa_2 R_{\mu\nu}\phi^{,\mu}\phi^{,\nu}$ where…

The aim of this paper is to introduce a new weak separation axiom that generalizes the separation properties between $T_1$ and completely Hausdorff. We call a topological space $(X,\tau)$ a $T_{\kappa,\xi}$-space if every compact subset of…

We give relations for the embedding of spatially-flat Friedmann-Robertson-Walker cosmological models of Einstein's theory in flat manifolds of the type used in Kaluza-Klein theory. We present embedding diagrams that depict different 4D…

For many purposes, a three-dimensional foliation of spacetime is more advantageous to understanding its light cone structure. We derive the equations describing such foliations for the Kerr geometry with non-zero cosmological constant, and…