Related papers: On the equivalence of linear sets

Let $f, g: \mathbb{R}^2 \to \mathbb{R}$ be two submersion functions and $\mathscr{F}(f)$ and $\mathscr{F}(g)$ be the regular foliations of $\mathbb{R}^2$ whose leaves are the connected components of the levels sets of $f$ and $g$,…

To every Gorenstein algebra $A$ of finite vector space dimension greater than 1 over a field $\FF$ of characteristic zero, and a linear projection $\pi$ on its maximal ideal ${\mathfrak m}$ with range equal to the annihilator…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field and $A$ a standard graded $S$-algebra. In terms of the Gr\"obner basis of the defining ideal $J$ of $A$ we give a condition, called the x-condition, which implies that all graded…

In the present paper, we define and study $C$-parallel and $C$-proper slant curves of $S$-manifolds. We prove that a curve $\gamma $ in an $S$-manifold of order $r\geq 3,$ under certain conditions, is $C$-parallel or $C$-parallel in the…

We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of…

Let $\Gamma$ be an abelian group and $g \geq h \geq 2$ be integers. A set $A \subset \Gamma$ is a $C_h[g]$-set if given any set $X \subset \Gamma$ with $|X| = k$, and any set $\{ k_1 , \dots , k_g \} \subset \Gamma$, at least one of the…

Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution…

We consider the following extension of the classical Liouville theorem: A calibration $\omega \in \Lambda^n \mathbb{R}^m$, where $3 \le n \le m$, has the Liouville property if a Sobolev mapping $F\colon \Omega \to \mathbb{R}^m$, where…

Given a Riemannian manifold $M$ endowed with a smooth metric $g$ satisfying upper and lower sectional curvature bounds, we show an equivalence property between the $\mathrm{L}^2$ norm on $M$ and the $\mathrm{L}^2$ norm on subsets $\omega$…

Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the Higgs-family symmetries Z2, U(1) and SO(3) are discussed. Sufficient and necessary…

For an incidence geometry $\mathcal{G} = (\mathcal{P}, \mathcal{L}, \text{I})$ with a linear representation $\mathcal{T}_n^*(\mathcal{K})$, we apply WQH switching to construct a non-geometric graph $\Gamma'$ cospectral with the line graph…

Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear…

Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if dim M is greater than or equal to 5 and if dim M = 5, then k= 2 at all points. We…

If $\phi: L\to L'$ is a bijection from the set of lines of a linear space $(P,L)$ onto the set of lines of a linear space $(P',L')$ ($\dim P, \dim P'\geq 3$), such that intersecting lines go over to intersecting lines in both directions,…

We carry out the programme of R. Liouville \cite{Liouville} to construct an explicit local obstruction to the existence of a Levi--Civita connection within a given projective structure $[\Gamma]$ on a surface. The obstruction is of order 5…

Given two parallelisms of a projective space we describe a construction, called blending, that yields a (possibly new) parallelism of this space. For a projective double space $(\mathbb{P},\parallel_\ell,\parallel_r)$ over a quaternion skew…

We construct nontrivial L-equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L-equivalence for curves (necessarily over…

A homemorphism between domains in $\mathbb R^n$, $n\ge 2$ is quasiconformal, with its intricate analytic and geometric consequences, if the (pointwise) linear dilatation -- a purely metric quantity -- is uniformly bounded. Gehring proved…

We consider decomposition spaces $\R^3/G$ that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on $\R^3/G$ constructed via modular embeddings into Euclidean spaces promote the controlled topology…

Let $p$ be a prime and $q = p^k$. A subset $\mathcal{F} \subset \operatorname{\Gamma L}_{2}(q)$ is intersecting if any two semilinear transformations in $\mathcal{F}$ agree on some non-zero vector in $\mathbb{F}_q^2$. We show that any…