Related papers: Quantitative Transversal Theorems in the Plane
We give new necessary and sufficient conditions for higher order convex ordering. These results generalize the Levin-Ste\v{c}kin theorem (1960) on convex ordering. The obtained results can be useful in the study of the Hermite-Hadamard type…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…
We prove that if a subset of a $d$-dimensional vector space over a finite field with $q$ elements has more than $q^{d-1}$ elements, then it determines all the possible directions. If a set has more than $q^k$ elements, it determines a…
We introduce a new ``Winding Number Conjecture'' about maps from the $(d-1)$-skeleton of the $((d+1)(q-1))$-simplex into $\real^d$. This conjecture is equivalent to the Topological Tverberg Theorem. Furthermore, many statements about the…
In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg…
Let $X$ be a smooth irreducible projective variety of dimension at least 2 over an algebraically closed field of characteristic 0 in the projective space ${\mathbb{P}}^n$. Bertini's Theorem states that a general hyperplane $H$ intersects…
In this article, we study hypersurfaces $\Sigma\subset \mathbb{R}^{n+1}$ with constant weighted mean curvature. Recently, Wei-Peng proved a rigidity theorem for CWMC hypersurfaces that generalizes Le-Sesum classification theorem for…
A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its \'etale endomorphisms are proper. We study the conjecture for $\mathbb{Q}$-acyclic surfaces of negative Kodaira dimension. We show that $G$-equivariant…
A family of sets has the $(p,q)$ property if among any $p$ members of the family some $q$ have a nonempty intersection. It is shown that for every $p\ge q\ge d+1$ there is a $c=c(p,q,d)<\infty$ such that for every family $\scr F$ of…
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be…
Menger's theorem says that, for $k\ge0$, if $S, T$ are sets of vertices in a graph $G$, then either there are $k + 1$ vertex-disjoint paths between $S$ and $T$, or there is a set X of at most $k$ vertices such that every $S$-$T$ path passes…
The paper studies 'good arrangements' (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties…
Based on the principle of relativity, we find that the sufficient and necessary condition for the general covariance of a field theory actually requires more than the invariance of its local Langrangian density. If the spacetime is not a…
Worldline quantum inequalities provide lower bounds on weighted averages of the renormalised energy density of a quantum field along the worldline of an observer. In the context of real, linear scalar field theory on an arbitrary globally…
In this research article, we formulate and prove multidimensional Widder--Arendt theorem and integrated form of multidimensional Widder--Arendt theorem for functions with values in sequentially complete locally convex spaces. Established…
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed,…
We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between sequences of vectors in the first Hilbert space with a vector…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
The article proves the Infinitesimal Torelli theorem for surfaces subject to the following conditions: 1) the canonical bundle of a surface is ample and generated by its global sections, 2)the geometric genus $p_g \geq 4$, 3) the…
We establish a transversality theorem for multiple-point crossings under generic linear perturbations with explicit Hausdorff measure estimates for the exceptional parameter set, and hence explicit upper bounds on its Hausdorff dimension.…