相关论文: An Elementary Proof of the Minimal Euclidean Funct…

Let $M$ be an $n$-dimensional smooth oriented complete embedded minimal hypersurface in $\mathbb{R}^{n+1}$ with Euclidean volume growth. We show that if the image under the Gauss map of $M$ avoids some neighborhood of a half-equator, then…

Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence…

We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the conjecture in length four and five, in low codimension. We…

A quadrangular embedding of a graph in a surface $\Sigma$, also known as a quadrangulation of $\Sigma$, is a cellular embedding in which every face is bounded by a $4$-cycle. A quadrangulation of $\Sigma$ is minimal if there is no…

Let $A_{\varphi}$ denote the matrix of rotation with angle $\varphi$ of the Euclidean plane, FLOOR the function, which rounds a real point to the nearest lattice point down on the left and ROUND the function for rounding off a vector to the…

Function field lattices are an interesting example of algebraically constructed lattices. Their minimum distance is bounded below by a function of the gonality of the underlying function field. Known explicit examples--coming mostly from…

For any $\Lambda>0$, let $\mathcal{M}_{n,\Lambda}$ denote the space containing all locally Lipschitz minimal graphs of dimension $n$ and of arbitrary codimension $m$ in Euclidean space $\mathbb{R}^{n+m}$ with uniformly bounded 2-dilation…

For $n\geq 4$ (even), the function $\varphi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the unit disk $\mathbb{D}$ onto a domain bounded by an epicycloid with $n-1$ cusps. In this paper, the class $\mathcal{S}^*_{n\mathcal{L}} =…

Denote by $E_\epsilon$ the Ginzburg-Landau functional in the plane and let $\tilde u_\varepsilon$ be the radial solution to the Euler equation associated to the problem $\min \left\{E_\varepsilon(u,B_1): \>\left. u\right\vert _{\partial…

A simple graph G is said to be representable in a real vector space of dimension m if there is an embedding of the vertex set in the vector space such that the Euclidean distance between any two distinct vertices is one of only two distinct…

Two themes associated with invariant measures on the matrix groups ${\rm SL}_N(\mathbb F)$, with $\mathbb F = \mathbb R, \mathbb C$ or $\mathbb H$, and their corresponding lattices parametrised by ${\rm SL}_N(\mathbb F)/{\rm SL}_N(\mathbb…

In the work \cite{Laredo} the author shows that every hypersurface in Euclidean space is locally associated to the unit sphere by a sphere congruence, whose radius function $R$ is a geometric invariant of hypersurface. In this paper we…

Define the minimal excludant of an overpartition $\pi$, denoted $ \overline{\text{mex}}(\pi)$, to be the smallest positive integer that is not a part of the non-overlined parts of $\pi$. For a positive integer $n$, the function…

Let $K$ be a algebraically closed field of characteristic 0 that is complete with respect to a non-Archimedean absolute value. Let $\phi\in K(z)$ with $\textrm{deg}(\phi)\geq 2$. In this paper we establish uniform logarithmic…

We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures. In particular, we define local angle functions encoding…

Let $\Sigma_g$ be a closed Riemann surface of genus $g$. Let $G$ be a finite subgroup of the automorphism group of $\Sigma_g$. It is well known that there exists a smooth $G$-equivariant embedding from $\Sigma_g$ to some Euclidean space…

The generalized group of units of the ring modulo $n$ was first introduced by El-Kassar and Chehade, written as $U^k(Z_n)$. This allows us to formulate a new generalization to the Euler phi function $\varphi(n)$, that represents the order…

For a unit vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$, $n\geq 1$, we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gauss map of the immersion. When the hypersurface is the unit…

Let $\phi(x, y)\colon \mathbb{R}^d\times \mathbb{R}^d\to \mathbb{R}$ be a function. We say $\phi$ is a Mattila--Sj\"{o}lin type function of index $\gamma$ if $\gamma$ is the smallest number satisfying the property that for any compact set…

Let $\phi(n)$ be the Euler-phi function, define $\phi_0(n) = n$ and $\phi_{k+1}(n)=\phi(\phi_{k}(n))$ for all $k\geq 0$. We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $\phi_k(n)$ is $y$-smooth,…