  We study a version of the strong minimum principle, and large time
asymptotics of positive viscosity solutions to classes of doubly nonlinear
parabolic equations of the form $$ H(Du,D^2u)-u^{k-1}u_t=0,\;\;k\geq
1,\quad\mbox{in $\Omega\times [0,T)$},$$ where $\Omega\subset \mathbb{R}^n$ is
a bounded domain and $0<T\leq \infty$. The spatial operator $H$ is homogeneous
with power $k$.
