The volume of the intersection of a convex body with its translates

M. Meyer; S. Reisner; M. Schmuckenschläger

doi:10.1112/S0025579300007051

The volume of the intersection of a convex body with its translates

M. Meyer, S. Reisner, M. Schmuckenschläger

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is proved that for a symmetric convex body K in Rn, if for some [formula omitted] depends on [formula omitted] then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies are studied.

Original language	English
Pages (from-to)	278-289
Number of pages	12
Journal	Mathematika
Volume	40
Issue number	2
DOIs	https://doi.org/10.1112/S0025579300007051
State	Published - 1993

Bibliographical note

Funding Information:
Dr. Schmuckenschlager acknowledges support from an Erwin Schrodinger stipendium, held at the Johannes Kepler Universitat, Linz, Austria.

ASJC Scopus subject areas

General Mathematics

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10.1112/S0025579300007051

Cite this

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title = "The volume of the intersection of a convex body with its translates",

abstract = "It is proved that for a symmetric convex body K in Rn, if for some [formula omitted] depends on [formula omitted] then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies are studied.",

author = "M. Meyer and S. Reisner and M. Schmuckenschl{\"a}ger",

note = "Funding Information: Dr. Schmuckenschlager acknowledges support from an Erwin Schrodinger stipendium, held at the Johannes Kepler Universitat, Linz, Austria.",

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AU - Meyer, M.

AU - Reisner, S.

AU - Schmuckenschläger, M.

N1 - Funding Information: Dr. Schmuckenschlager acknowledges support from an Erwin Schrodinger stipendium, held at the Johannes Kepler Universitat, Linz, Austria.

PY - 1993

Y1 - 1993

N2 - It is proved that for a symmetric convex body K in Rn, if for some [formula omitted] depends on [formula omitted] then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies are studied.

AB - It is proved that for a symmetric convex body K in Rn, if for some [formula omitted] depends on [formula omitted] then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies are studied.

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U2 - 10.1112/S0025579300007051

DO - 10.1112/S0025579300007051

M3 - Article

AN - SCOPUS:84976074615

SN - 0025-5793

VL - 40

SP - 278

EP - 289

JO - Mathematika

JF - Mathematika

IS - 2

ER -

The volume of the intersection of a convex body with its translates

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

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