Mean Lattice Point Discrepancy Bounds, Ii: Convex Domains in the Plane
نویسندگان
چکیده
We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.
منابع مشابه
A convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
متن کاملA Brunn-minkowski Inequality for the Integer Lattice
A close discrete analog of the classical Brunn-Minkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a method for computing the exact lower bound in this situation, given the dimension of the lattice and the cardinal...
متن کاملThe Elastic Torsion Problem: Solutions in Convex Domains
The torsion function of a plane domain is a function which is zero on the boundary of the domain and whose Laplacian is minus one at every point in the interior of the domain. We survey qualitative properties of the torsion function, and bounds on it and its derivatives, available when the plane domain is convex.
متن کاملOn the streaming complexity of fundamental geometric problems
In this paper, we focus on lower bounds and algorithms for some basic geometric problems in the one-pass (insertion only) streaming model. The problems considered are grouped into three categories — (i) Klee’s measure (ii) Convex body approximation, geometric query, and (iii) Discrepancy Klee’s measure is the problem of finding the area of the union of hyperrectangles. Under convex body approxi...
متن کاملOptimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004