On bodies with congruent sections by cones or non-central planes

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Non-intersection Bodies All of Whose Central Sections Are Intersection Bodies

We construct symmetric convex bodies that are not intersection bodies, but all of their central hyperplane sections are intersection bodies. This result extends the studies by Weil in the case of zonoids and by Neyman in the case of subspaces of Lp.

متن کامل

Unique Determination of Convex Polytopes by Non-central Sections

A question of Barker and Larman asks whether convex bodies that contain a sphere of radius t in their interiors are uniquely determined by the volumes of sections by hyperplanes tangent to the sphere. We affirmatively solve this problem for convex polytopes.

متن کامل

Coassociative Cones That Are Ruled by 2-planes

It is shown that coassociative cones in R7 that are r-oriented and ruled by 2-planes are equivalent to CR-holomorphic curves in the oriented Grassmanian of 2-planes in R7. The geometry of these CR-holomorphic curves is studied and related to holomorphic curves in S6. This leads to an equivalence between associative cones on one side and the coassociative cones whose second fundamental form has ...

متن کامل

On the Busemann-Petty Problem Concerning Central Sections of Centrally Symmetric Convex-Bodies

We present a method which shows that in E3 the Busemann-Petty problem, concerning central sections of centrally symmetric convex bodies, has a positive answer. Together with other results, this settles the problem in each dimension. In [BP], Busemann and Petty asked the following question, which resulted from reformulating a problem in Minkowskian geometry. Suppose K\ and K2 are convex bodies i...

متن کامل

Euclidean sections of convex bodies

This is a somewhat expanded form of a four hours course given, with small variations, first at the educational workshop Probabilistic methods in Geometry, Bedlewo, Poland, July 6-12, 2008 and a few weeks later at the Summer school on Fourier analytic and probabilistic methods in geometric functional analysis and convexity, Kent, Ohio, August 13-20, 2008. The main part of these notes gives yet a...

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

ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 2018

ISSN: 0002-9947,1088-6850

DOI: 10.1090/tran/7395