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

Sharp bounds are given for solutions to the minimal surface equation with vanishing boundary values over domains containing sectors of opening bigger than pi.

We give asymptotic bounds for the optimal Lipschitz constants for the systole map from the Teichmuller space to the curve complex. We give similar results to those known for closed surfaces in the cases when the genus is fixed or the ratio…

The main purpose of the note is to exclude the existence of certain submaximal curves in fake projective planes. This will lead to lower bounds on multipoint Seshadri constants of `fake' $\mathcal{O}(1)$ on fake projective planes.

We improve the best lower bounds on the chromatic number of Euclidean space in small dimensions. The new results depend on extensive computations in Sage.

Given a smooth complex projective variety $X$ and an ample line bundle $L$ on $X$. Fix a point $x\in X$. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of $L$ at $x$, i.e $\eps(L,x)=\root…

Let $X_r$ denote the blow-up of the hyperelliptic surface $X$ at $r$ very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on $X_r$ and compare it with an existing result. We then study the…

The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general…

We provide a lower bound on the degree of curves of the projective plane $\mathbb{P}^2$ passing through the centers of a divisorial valuation $\nu$ of $\mathbb{P}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type…

We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the $N$-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain…

We define Seshadri constants for Higgs bundles on smooth projective varieties over algebraically closed fields of characteristic zero. This definition is inspired by and analogous to the notion of Seshadri constants for ordinary vector…

We prove sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times in various contexts. An upper bound for the genus of stable surfaces in the electrostatic system is provided. We also study the…

We simplify Ciliberto's and Miranda's method(arXiv:0812.0032) to construct degenerations of $\mathbb{CP}^2$ blown up in several points yielding lower bounds of the corresponding multi-point Seshadri constants. In particular we exploit an…

In analogy to the relation between symplectic packings and symplectic blow ups we show that multiple point Seshadri constants on projective complex surfaces can be calculated as the supremum of radii of multiple K\"ahler ball embeddings.

We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.

Based on the theory of an infinitesimal Newton-Okounkov body, we extend the results of Lazarsfeld-Pareschi-Popa on abelian surfaces. Moreover, we show that the higher syzygies of $(X,L)$ are completely determined by its Seshadri constant…

In this note, we study Seshadri constants and Gromov widths of toric surfaces via lattice widths of their moment polygons. We give the sharp lower bound of the ratio between the Gromov width of a symplectic toric $4$-fold and the lattice…

The paper is concerned with sharp estimates of constants in Poincare type inequalities for functions having zero mean value on the boundary of a Lipschitz domain or on a measurable part of it. These estimates are useful for various…

In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.

We obtain an upper bound for the number of critical points of the systole function on $\mathcal{M}_g$. Besides, we obtain an upper bound for the number of those critical points whose systole is smaller than a constant.

We prove several results about the multiplicity of the first Steklov eigenvalues on compact surfaces with boundary. We improve some bounds on the multiplicity, especially for the first eigenvalue, and we prove they are sharp on some…