2018
Dec
19

# Analysis Seminar: Dmitry Ryabogin (Kent) "On a local version of the fifth Busemann-Petty Problem"

12:00pm to 1:00pm

## Location:

Ross Building, Room 70

Title: On a local version of the fifth Busemann-Petty Problem

Abstract:

In 1956, Busemann and Petty posed a series of questions about symmetric convex bodies, of which only the first one has been solved. Their fifth problem asks the following.

Let K be an origin symmetric convex body in the n-dimensional Euclidean space and let H_x be a hyperplane passing through the origin orthogonal to a unit direction x. Consider a hyperplane G parallel to H_x and supporting to K and let

C(K,x)=vol(K\cap H_x)dist (0, G).

Abstract:

In 1956, Busemann and Petty posed a series of questions about symmetric convex bodies, of which only the first one has been solved. Their fifth problem asks the following.

Let K be an origin symmetric convex body in the n-dimensional Euclidean space and let H_x be a hyperplane passing through the origin orthogonal to a unit direction x. Consider a hyperplane G parallel to H_x and supporting to K and let

C(K,x)=vol(K\cap H_x)dist (0, G).