Unique Determination of Convex Polytopes by Non-central Sections

نویسنده

  • V. YASKIN
چکیده

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.

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

Normal polytopes

In Section 1 we overview combinatorial results on normal polytopes, old and new. These polytopes represent central objects of study in the contemporary discrete convex geometry, on the crossroads of combinatorics, commutative algebra, and algebraic geometry. In Sections 2 and 3 we describe two very different possible ways of advancing the theory of normal polytopes to next essential level, invo...

متن کامل

On Perimeters of Sections of Convex Polytopes

In his book “Geometric Tomography” Richard Gardner asks the following question. Let P and Q be origin-symmetric convex bodies in R whose sections by any plane through the origin have equal perimeters. Is it true that P = Q? We show that the answer is “Yes” in the class of origin-symmetric convex polytopes. The problem is treated in the general case of R.

متن کامل

The Perles-Shephard identity for non-convex polytopes

Using the theory of valuations, we establish a generalization of an identity of Perles-Shephard for non-convex polytopes. By considering spherical valuations, we obtain the Gram-Euler, Descartes and Euler-Poincar e theorems for non-convex polytopes.

متن کامل

Asymptotic approximation of smooth convex bodies by general polytopes

For the optimal approximation of convex bodies by inscribed or circumscribed polytopes there are precise asymptotic results with respect to different notions of distance. In this paper we want to derive some results on optimal approximation without restricting the polytopes to be inscribed or circumscribed. Let Pn and P(n) denote the set of polytopes with at most n vertices and n facets, respec...

متن کامل

Central Limit Theorems for Random Polytopes

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

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 2012