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In this paper, our purpose is to study rigidity theorems for $\lambda$-hypersurfaces in Euclidean space under Gauss map. As a Bernstein type problem for $\lambda$-hypersurfaces, we prove that an entirely graphic $\lambda$-hypersurface in…
The famous Ham-Sandwich theorem states that any $d$ point sets in $\mathbb{R}^d$ can be simultaneously bisected by a single hyperplane. The $\alpha$-Ham-Sandwich theorem gives a sufficient condition for the existence of biased cuts, i.e.,…
In this paper we study measure theoretical size of the image of naturally embedded vector bundles in $\mathbb{R}^{n} \times \mathbb{R}^{n}$ under the codiagonal morphism, i.e. $\Delta_{*}$ in the category of finite dimensional…
One of the earliest results in enumerative combinatorial geometry is the following theorem of de Bruijn and Erd\H{o}s: Every set of points $E$ in a projective plane determines at least $|E|$ lines, unless all the points are contained in a…
This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space,…
This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree…
In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region…
We present bijections for the planar cases of two counting formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-slide" operation. This is the first time a bijective proof is…
Let M be a (bounded or not) domain of C^n which is complete with respect to a K\"ahler metric, or more generally, a complete K\"ahler manifold with trivial canonical bundle. Let f be a linearly nondegenerate meromorphic map from M to the…
A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making…
In this paper we show an abundance of complete K\"ahler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved…
The localization of vector multiplets is examined using the {\cal N}=1 supersymmetric U(1) gauge theory with the Fayet-Iliopoulos term coupled to charged chiral multiplets in four dimensions. The vector field becomes localized on a BPS wall…
We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their…
The purpose of this paper is twofold. In the first part we concentrate on hyperplane sections of algebraic schemes, and present results for determining when Gr\"obner bases pass to the quotient and when they can be lifted. The main…
We study k-very ampleness of line bundles on blow-ups of hyperelliptic surfaces at r very general points. We obtain a numerical condition on the number of points for which a line bundle on the blow-up of a hyperelliptic surface at these r…
How can a stack of identical blocks be arranged to extend beyond the edge of a table as far as possible? We consider a generalization of this classic puzzle to blocks that differ in width and mass. Despite the seemingly simple premise, we…
In this paper we develop a complete theory of factorization for isometries of hyperbolic 4-space. Of special interest is the case where a pair of isometries is linked, that is, when a pair of isometries can be expressed each as compositions…
Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The…