@misc{10481/106321,
year = {2025},
month = {8},
url = {https://hdl.handle.net/10481/106321},
abstract = {A surface 
Σ
 in the hyperbolic space 
H
3
 is called a horo-shrinker if its mean curvature 
H
 satisfies 
H
=
⟨
N
,
∂
z
⟩
, where 
(
x
,
y
,
z
)
 are the coordinates of 
H
3
 in the upper half-space model and 
N
 is the unit normal of 
Σ
. In this paper we study horo-shrinkers invariant by one-parameter groups of isometries of 
H
3
 depending if these isometries are hyperbolic, parabolic or spherical. We characterize totally geodesic planes as the only horo-shrinkers invariant by a one-parameter group of hyperbolic translations along vertical geodesic tangent to 
∂
z
. The grim reapers are defined as the horo-shrinkers invariant by a one-parameter group of parabolic translations perpendicular to 
∂
z
. We describe the geometry of the grim reapers proving that they are periodic surfaces. In the last part of the paper, we give a complete classification of horo-shrinkers invariant by spherical rotations about the 
z
-axis, distinguishing if the surfaces intersect or not the rotation axis.},
organization = {MCIN/AEI/10.13039/501100011033/ - ERDF (PID2021-124157NB-I00)},
organization = {CARM, Programa Regional de Fomento de la Investigación, Fundación Séneca-Agencia de Ciencia y Tecnología Región de Murcia (reference 21937/PI/22)},
organization = {MINECO/MICINN/FEDER (grant no. PID2023-150727NB-I00)},
organization = {MCINN/AEI/10.13039/501100011033 - “María de Maeztu” Excellence Unit IMAG (CEX2020-001105-M)},
publisher = {Mathematical Society of the Republic of China},
title = {Horo-shrinkers in the Hyperbolic Space},
doi = {10.11650/tjm/250707},
author = {Bueno, Antonio and López Camino, Rafael},
}