6533b7d2fe1ef96bd125e27c
RESEARCH PRODUCT
Total curvatures of convex hypersurfaces in hyperbolic space
A A BorisenkoVicente Miquelsubject
Hyperbolic groupGeneral MathematicsHyperbolic spaceHyperbolic 3-manifoldMathematical analysisHyperbolic angleMathematics::Metric GeometryHyperbolic manifoldUltraparallel theoremHyperbolic triangleRelatively hyperbolic groupMathematicsdescription
We give sharp upper estimates for the difference circumradius minus inradius and for the angle between the radial vector (respect to the center of an inball) and the normal to the boundary of a compact $h$-convex domain in the hyperpolic space. We apply these estimates to get the limit at the infinity for the quotients Volume/Area and (Total $k$-mean curvature)/Area of a family of $h$-convex domains which expand over the whole space. The theorem for the first quotient gives an extension to arbitrary dimension of a result of Santalo and Yanez for the hyperbolic plane.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-03-01 | Illinois Journal of Mathematics |