Related papers: An effective and sharp lower bound on Seshadri con…

We provide a lower bound for the first eigenvalue of the Laplace-Beltrami operator on a closed orientable hypersurface minimally embedded in an orientable compact Riemannian manifold with Ricci curvature bounded below by a positive…

We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak approximation. To do so, we exploit the relationship between…

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known…

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 consider a real del Pezzo surface without points. We prove that the same surface over complex numbers field $\mathbb{C}$ has Picard number is at least two.

We prove that the Hilbert property is satisfied by certain del Pezzo surfaces of degree one and Picard rank 1 over fields finitely generated over $\mathbb{Q}$. We generalize results of the first author on elliptic surfaces and employ…

We improve a bound due to the second author on number of rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact…

In this talk I summarize a recently proposed mechanism to understand pi pi scattering to 1 GeV. The model is motivated by the 1/Nc expansion to QCD, and includes a current algebra contact term and resonant pole exchanges. Chiral symmetry…

Let $X^n_{r,s}$ denote the blow-up of $\mathbb{P}^n$ along $r$ general lines and $s$ general points. In this paper, we focus on $l$-very ample line bundles on $X^n_{0,s}$ and investigate their Seshadri constants with some restrictions on…

We establish effective bounds on the number of periodic points of degree-$d$ polynomials $\phi$ defined over $p$-adic fields and number fields, under a mild reduction hypothesis that is satisfied by all unicritical polynomials $X^d + c$…

We study the convergence analysis of a Picard-S iteration method for a particular class of weak-contraction mappings. Furthermore, we prove a data dependence result for fixed point of the class of weak-contraction mappings with the help of…

For an oriented surface $S$, the singular set of a fold map $f:S\rightarrow \mathbb{R}^2$ is a collection of smooth curves, also known as fold singularities. We construct a sharp lower bound on the number of self-intersections of such fold…

We characterize all compact embedded stable minimal capillary surfaces with capillary angle close to either $0$ or $\pi$ that are supported on a complete embedded minimal surface with finite total curvature that is not an affine plane.…

We study the behavior of geometric Picard ranks of K3 surfaces over the rationals under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes $p<2^{16}$ in several representative…

Ellingsrud and Peskine (1989) proved that there exists a bound on the degree of smooth non general type surfaces in P^4. The latest proven bound is 52 by Decker and Schreyer in 2000. In this paper we consider bounds on the degree of a…

Let $X$ be a smooth complex projective curve, and let $E$ be a vector bundle on $X$ which is not semistable. For a suitably chosen integer $r$, let $\text{Gr}(E)$ be the Grassmann bundle over $X$ that parametrizes the quotients of the…

We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of a compact manifold and the Euclidean space with the flat metric, $(M^m\times \mathbb{R}^n,g+g_E)$, $m,n>1$. In particular, we introduce a lower…

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…

Let $X$ be a projective surface and let $L$ be an ample line bundle on $X$. The global Seshadri constant $\varepsilon(L)$ of $L$ is defined as the infimum of Seshadri constants $\varepsilon(L,x)$ as $x\in X$ varies. It is an interesting…