2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74495The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in $\mathbb{R}^n$ with smaller volume of all $k$-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer to this question is negative if $k>3$. The problem is still open for $k=2,3$. In this article we formulate and completely solve the lower dimensional Busemann-Petty problem in the hyperbolic space $\mathbb{H}^n$.12 pages, 2 figuresFunctional AnalysisMetric Geometry52A55, 52A20, 46B20text