  For a function $f$ which foliates a one-sided neighbourhood of a closed
hypersurface $M$, we give an estimate of the distance of $M$ to a Wulff shape
in terms of the $L^{p}$-norm of the traceless $F$-Hessian of $f$, where $F$ is
the support function of the Wulff shape. This theorem is applied to prove
quantitative stability results for the anisotropic Heintze-Karcher inequality,
the anisotropic Alexandrov problem, as well as for the anisotropic
overdetermined boundary value problem of Serrin-type.

Analysis of PDEs;Differential Geometry