Journal of Differential Geometry
- J. Differential Geom.
- Volume 110, Number 2 (2018), 187-220.
The floating body in real space forms
We carry out a systematic investigation on floating bodies in real space forms. A new unifying approach not only allows us to treat the important classical case of Euclidean space as well as the recent extension to the Euclidean unit sphere, but also the new extension of floating bodies to hyperbolic space.
Our main result establishes a relation between the derivative of the volume of the floating body and a certain surface area measure, which we called the floating area. In the Euclidean setting the floating area coincides with the well known affine surface area, a powerful tool in the affine geometry of convex bodies.
The first author is supported by the European Research Council, project number 306445.
The second author is partially supported by an NSF grant.
J. Differential Geom., Volume 110, Number 2 (2018), 187-220.
Received: 26 April 2016
First available in Project Euclid: 6 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 52A55: Spherical and hyperbolic convexity
Secondary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 53A35: Non-Euclidean differential geometry
Besau, Florian; Werner, Elisabeth M. The floating body in real space forms. J. Differential Geom. 110 (2018), no. 2, 187--220. doi:10.4310/jdg/1538791243. https://projecteuclid.org/euclid.jdg/1538791243