In this paper, it is shown that a closed surface in 3-dimensional harmonic conformally flat space is minimal if the sign of the mean curvature does not change. Also, it is determined that the critical point of mean curvature functional of the surface is homeomorphic to the sphere.
MOSADEGH, NAJMA and ABEDI, ESMAIEL
"Variational geometry for surfaces in conformally flat space,"
Turkish Journal of Mathematics: Vol. 46:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss1/3