This is an announcement for the paper "A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space" by V.Yaskin. Abstract: The 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 $\mathbb{H}^n$. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 52A55, 52A20, 46B20 Remarks: 12 pages, 2 figures The source file(s), LDHBP.tex: 70816 bytes, pic04.eps: 9457 bytes, pic06.eps: 9542 bytes, is(are) stored in gzipped form as 0503289.tar.gz with size 25kb. The corresponding postcript file has gzipped size 59kb. Submitted from: yaskinv@math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0503289 or http://arXiv.org/abs/math.FA/0503289 or by email in unzipped form by transmitting an empty message with subject line uget 0503289 or in gzipped form by using subject line get 0503289 to: math@arXiv.org.