Isoperimetric Regions in the Hyperbolic Plane Between Parallel Horocycles

Horocycles in hyperbolic 3-manifolds

A Free Boundary Isoperimetric Problem in the Hyperbolic Space between Parallel Horospheres

In this work we investigate the following isoperimetric problem: to find the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the area of the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by stud...

Support Theorems for Horocycles on Hyperbolic Spaces

(i) An explicit description of the range D(X)̂where X is a Euclidean space or a symmetric space of the noncompact type ([2], [3]). Here (D = Cc ). In the first case, f̂ in (1.1) is integration over hyperplanes in X = Rn; in the latter case f̂ in (1.1) refers to integration over horocycles ξ in the symmetric space X. (ii) Medical application in X-ray reconstruction ([6], p.47). (iii) Existence theo...

Isoperimetric Regions in Spaces

We examine the least-perimeter way to enclose given area or volume in various spaces including some spaces with density.

Isoperimetric Regions in Cones

We consider cones C = 0 × Mn and prove that if the Ricci curvature of C is nonnegative, then geodesic balls about the vertex minimize perimeter for given volume. If strict inequality holds, then they are the only stable regions.