@misc{10481/105398,
year = {2025},
month = {7},
url = {https://hdl.handle.net/10481/105398},
abstract = {If α ∈ R, an α-stationary surface in Euclidean space is a surface   whose mean curvature
H satisfies H ( p) = α| p| −2〈ν, p〉, p ∈  . These surfaces generalize in dimension two a
classical family of curves studied by Euler which are critical points of the moment of inertia
of planar curves. In this paper we establish, via inversions, a one-to-one correspondence
between α-stationary surfaces and −(α + 4)-stationary surfaces. In particular, there is a
correspondence between −4-stationary surfaces and minimal surfaces. Using this duality we
give some results of uniqueness of −4-stationary surfaces and we solve the Börling problem.},
organization = {MINECO/MICINN/FEDER  PID2023-150727NB-I00},
organization = {MCINN/AEI/10.13039/501100011033/CEX2020-001105-M CEX2020-001105-M},
organization = {Universidad de Granada/CBUA},
publisher = {Springer Nature},
keywords = {Euler’s problem},
keywords = {Minimal surfaces},
keywords = {Inversions},
keywords = {Tangency principle},
title = {A connection between minimal surfaces and the two-dimensional analogues of a problem of Euler},
doi = {10.1007/s10231-025-01593-w},
author = {López Camino, Rafael},
}