Related papers: Restrictions on Seshadri constants on surfaces

In this article, we give computable lower bounds for the first non-zero Steklov eigenvalue $\sigma_1$ of a compact connected 2-dimensional Riemannian manifold $M$ with several cylindrical boundary components. These estimates show how the…

We extend known methods to establish upper bounds on the least character non-residues contingent on different zero-free regions within the critical strip, in particular on bounded rectangles within the critical strip along the $\sigma=1$…

We investigate discrete Poincar\'e inequalities on piecewise polynomial subspaces of the Sobolev spaces H(curl) and H(div) in three space dimensions. We characterize the dependence of the constants on the continuous-level constants, the…

The goal of the paper is to sharpen and generalise bounds involving the Cheeger's isoperimetric constant $h$ and the first eigenvalue $\lambda_{1}$ of the Laplacian. A celebrated lower bound of $\lambda_{1}$ in terms of $h$,…

In this paper we obtain a bound on the number of isometry classes of finite area hyperbolic surfaces which are length isospectral to a given surface depending only on the topological type of the surface and the length of the shortest closed…

We show that for $k>1$ the number of genus $k$ minimal Lagrangians with area at most $A$ in a product of hyperbolic surfaces grows on the order of $A^{6(k-1)}$, with an explicit leading constant given in terms of the Mirzakhani function. We…

We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface…

We construct algebraic surfaces with a large number of type A singularities. Bivariate polynomials presented in previous works for the construction of nodal surfaces and certain families of Belyi polynomials are used. In some cases explicit…

We establish lower bounds for the sum of the reciprocals of eigenvalues of the Laplacian. For bounded domains, our result extends the upper bound provided by Bucur and Henrot on the second Neumann eigenvalue and is related to a result by…

New lower bounds on the minimum distance of quasi-twisted codes over finite fields are proposed. They are based on spectral analysis and eigenvalues of polynomial matrices. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a…

The goal of this work is to give new quantitative results about the distribution of semi-arithmetic hyperbolic surfaces in the moduli space of closed hyperbolic surfaces. We show that two coverings of genus $g$ of a fixed arithmetic surface…

We provide sharp bounds for the isoperimetric constants of infinite plane graphs (tessellations) with bounded vertex and face degrees. For example, if $G$ is a plane graph satisfying the inequalities $p_1 \leq \mbox{deg}\ v \leq p_2$ for $v…

Recently, Kothari et al.\ gave an algorithm for testing the surface area of an arbitrary set $A \subset [0, 1]^n$. Specifically, they gave a randomized algorithm such that if $A$'s surface area is less than $S$ then the algorithm will…

A differential operator introduced by A. Gray on the unit sphere bundle of a K\"ahler-Einstein manifold is studied. A lower bound for the first eigenvalue of the Laplacian for the Sasaki metric on the unit sphere bundle of a…

Let $X$ be a smooth projective variety defined over a field $k$ of characteristic $0$ and let $\mathcal{L}$ be a nef line bundle defined over $k$. We prove that if $x\in X$ is a $k$-rational point then the Seshadri constant $\epsilon(X,…

Starting from the data of a big line bundle $L$ on a projective manifold $X$ with a choice of $N\geq 1$ different points on $X$ we provide a new construction of $N$ Okounkov bodies which encodes important geometric features of ($L\to…

We investigate the asymptotic spectral distribution of the twisted Laplacian associated with a real harmonic 1-form on a compact hyperbolic surface. In particular, we establish a sublinear lower bound on the number of eigenvalues in a…

In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.

In contrast to elliptic surfaces, the Fourier restriction problem for hypersurfaces of non-vanishing Gaussian curvature which admit principal curvatures of opposite signs is still hardly understood. In fact, even for 2-surfaces, the only…

In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…