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Related papers: A note on multiple Seshadri constants on surfaces

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We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…

Analysis of PDEs · Mathematics 2023-12-08 Joonas Ilmavirta , Maarten V. de Hoop , Vitaly Katsnelson

We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if $f$ is a probability density on $\R^n$ of the form $f(x)=\prod_{i=1}^n f_i(x_i)$, where each $f_i$ is a density on $\R$, say…

Probability · Mathematics 2016-01-05 Galyna Livshyts , Grigoris Paouris , Peter Pivovarov

We prove that any ergodic $SL_2(R)$-invariant probability measure on a stratum of translation surfaces satisfies strong regularity: the measure of the set of surfaces with two non-parallel saddle connections of length at most $\epsilon_1,…

Dynamical Systems · Mathematics 2023-11-28 Benjamin Dozier

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…

Differential Geometry · Mathematics 2026-05-08 Ben Lowe , Fernando C. Marques , André Neves

In this article, we give a description of the closed cone of curves of the projective bundle $\mathbb{P}(E)$ over a smooth projective variety $X$. Using duality, we then calculate the nef cone of divisors in $\mathbb{P}(E)$ over some…

Algebraic Geometry · Mathematics 2022-08-19 Snehajit Misra , Nabanita Ray

The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili-Sire and…

Differential Geometry · Mathematics 2020-05-19 Mikhail Karpukhin , Nikolai Nadirashvili , Alexei V. Penskoi , Iosif Polterovich

It is well known that multi-point Seshadri constants for a small number $s$ of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for $s\geq 9$ points. Tackling the problem…

Algebraic Geometry · Mathematics 2016-02-08 Marcin Dumnicki , Brian Harbourne , Alex Küronya , Joaquim Roé , Tomasz Szemberg

We consider a maximization problem for eigenvalues of the Laplace-Beltrami operator on surfaces of revolution in $\mathbb{R}^3$ with two prescribed boundary components. For every $j$, we show that there is a surface $\Sigma_j$ which…

Spectral Theory · Mathematics 2016-11-23 Sinan Ariturk

We study the Restricted Solid on Solid model for surface growth in spatial dimension $d=2$ by means of a multi-surface coding technique that allows to produce a large number of samples of samples in the stationary regime in a reasonable…

Disordered Systems and Neural Networks · Physics 2016-11-28 Andrea Pagnani , Giorgio Parisi

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…

Differential Geometry · Mathematics 2010-11-16 François Fillastre

In dimensions $n\ge 2$ we obtain $L^{p_1}(\mathbb R^n) \times\dots\times L^{p_m}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide…

Classical Analysis and ODEs · Mathematics 2019-11-12 Georgios Dosidis

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…

Algebraic Geometry · Mathematics 2025-10-17 Juan García Escudero

The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…

Algebraic Geometry · Mathematics 2021-07-06 Diana Torres

In this article we obtain $L^2$ bounds for strongly singular integrals along curves in $\R^d;$ our results both generalise and extend to higher dimensions those obtained by Chandarana in the plane. Moreover, we show that the operators in…

Classical Analysis and ODEs · Mathematics 2007-05-23 Norberto Laghi , Neil lyall

This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…

Classical Analysis and ODEs · Mathematics 2021-03-29 Moritz Egert

Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very ampleness, and jet ampleness of linear systems of the form…

Algebraic Geometry · Mathematics 2026-03-24 Takumi Murayama

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…

Analysis of PDEs · Mathematics 2013-10-14 Georgios Psaradakis

We study asymptotic invariants of linear series on surfaces with the help of Newton-Okounkov polygons. Our primary aim is to understand local positivity of line bundles in terms of convex geometry. We work out characterizations of ample and…

Algebraic Geometry · Mathematics 2018-04-04 Alex Küronya , Victor Lozovanu

We study eigenvalues and eigenfunctions of the Laplacian on the surfaces of four of the regular polyhedrons: tetrahedron, octahedron, icosahedron and cube. We show two types of eigenfunctions: nonsingular ones that are smooth at vertices,…

Analysis of PDEs · Mathematics 2018-09-27 Evan Greif , Daniel Kaplan , Robert S. Strichartz , Samuel C. Wiese

We give a short, simple proof of maximal regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and the concept of R-boundedness for the resolvent.

Analysis of PDEs · Mathematics 2008-08-19 Thomas Krainer
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