  The purpose of this paper is to study the Schwarz-Pick type inequalities for
harmonic or pluriharmonic functions. By analogy with the generalized Khavinson
conjecture, we first give some sharp estimates of the norm of harmonic
functions from the Euclidean unit ball in $\mathbb{R}^n$ into the unit ball of
the real Minkowski space. Next, we give several sharp Schwarz-Pick type
inequalities for pluriharmonic functions from the Euclidean unit ball in
$\mathbb{C}^n$ or from the unit polydisc in $\mathbb{C}^n$ into the unit ball
of the Minkowski space. Furthermore, we establish some sharp coefficient type
Schwarz-Pick inequalities for pluriharmonic functions defined in the Minkowski
space. Finally, we use the obtained Schwarz-Pick type inequalities to discuss
the Lipschitz continuity, the Schwarz-Pick type lemmas of arbitrary order and
the Bohr phenomenon of harmonic or pluriharmonic functions.
