Heintze–Karcher and Jellett‐type theorems in conformally flat spaces.

In this paper, we consider a class of conformally flat spaces that includes the space forms as well as the doubled Schwarzschild space, and, we will prove an extension of Jellett's theorem. Next, we build an example, where the extension of Jellett's theorem does not hold. We also prove a Heintze–Karcher‐type inequality and we presented a one‐parametric family of conformally flat spaces, all distinct from space forms, where it holds a Heintze–Karcher‐type inequality. [ABSTRACT FROM AUTHOR]