Alexandrov's soap bubble theorem

Alexandrov's soap bubble theorem is a mathematical theorem from geometric analysis that characterizes a sphere through the mean curvature.

The theorem was proven in 1958 by Alexander Danilovich Alexandrov.

[1][2] In his proof he introduced the method of moving planes, which was used after by many mathematicians successfully in geometric analysis.

be a bounded connected domain with a boundary

with a constant mean curvature, then