The spherical convex floating body

Florian Besau; Elisabeth M. Werner

doi:10.1016/j.aim.2016.07.001

The spherical convex floating body

Florian Besau
, Elisabeth M. Werner

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

33 Scopus citations

Abstract

For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area turns out to be a spherical analogue to the classical affine surface area from affine differential geometry. Several properties of the floating area are established.

Original language	English (US)
Pages (from-to)	867-901
Number of pages	35
Journal	Advances in Mathematics
Volume	301
DOIs	https://doi.org/10.1016/j.aim.2016.07.001
State	Published - Oct 1 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Floating area
Spherical convex floating body
Spherical convexity

Publisher link

10.1016/j.aim.2016.07.001

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abstract = "For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area turns out to be a spherical analogue to the classical affine surface area from affine differential geometry. Several properties of the floating area are established.",

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AB - For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area turns out to be a spherical analogue to the classical affine surface area from affine differential geometry. Several properties of the floating area are established.

KW - Floating area

KW - Spherical convex floating body

KW - Spherical convexity

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SP - 867

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The spherical convex floating body

Abstract

Bibliographical note

Keywords

Publisher link

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