Ja n 20 07 On a question of Bourgain about geometric incidences ∗

نویسندگان

  • József Solymosi
  • Csaba D. Tóth
چکیده

Given a set of s points and a set of n lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, then we have s = Ω(n). This is the first nontrivial answer to a question recently posed by Jean Bourgain.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On a Question of Bourgain about Geometric Incidences

Given a set of s points and a set of n lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, then we have s = Ω(n). This is the first nontrivial answer to a question recently posed by Jean Bourgain.

متن کامل

Ja n 20 07 Embedding S n into R n + 1 with given integral Gauss curvature and optimal mass transport on S

In [3] A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data. The first goal of this paper is to give a variational solution to the problem of existence and uniqueness of a closed convex hypersurface in Euclidean space with prescribed integral Gauss curvature. Our solution includes the case of a convex polytop...

متن کامل

A new estimate for the topological degree

We establish a new estimate for the topological degree of continuous maps from the sphere SN into itself, which answers a question raised in Bourgain, Brezis, and Mironescu [Commun. Pure Appl. Math. 58 (2005) 529–551] and extends some of the results proved there, as well as in recent work by these authors (Lifting, degree, and distributional Jacobian revisited, http://ann.jussieu.fr/publication...

متن کامل

Ja n 20 05 Applications of the category of linear complexes of tilting modules associated with the category

We use the category of linear complexes of tilting modules for the BGG category O , associated with a semi-simple complex finitedimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category O(p,Λ).

متن کامل

Typology of Geometric Arrays of Human Figures’ Apparel in the Mina`i Pottery of the 6th and 7th Centuries AH.

Mina`i pottery produced in the late Seljuk and Khwarezmshahi periods under the supervision of pottery masters and painters, is more diverse and magnificent in terms of design and portrait than the previous works. In this group of pottery, human figures have a special place and are often seen in pottery. Various geometric patterns have been used in the apparel of these motifs, which has made ena...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007