I am reading by myself this paper and in the proof of the Theorem $6$ (it is on the page $7$), the authors stated
Thus, by the maximum principle for viscosity solutions, the solution $u_t$ to the geometric level set flow satisfies $u_t(x) \geq u_t(x^*)$ for all $x \in H_-^{\lambda}(\nu)$ and $t \geq 0$.
I looked for this maximum principle on the references of this paper and the best that I could find is the famous works by Evans and Spruck and Chen, Giga and Goto. Both works has
R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second-order partial differential equations, Arch. Rational Mech. Anal. 101 (1988) 1-27.
as a reference, then I believe that the Theorem $3.1$ on page $16$ of Jensen's paper is the maximum principle that I am looking for. What I would like to know is how exactly apply this maximum principle to the Theorem $6$ of the paper that I am reading. I do not have knowledge of the techniques applied to study viscosity solutions and the method of sup and sub solutions, then I will appreciate if you can explain with details how this maximum principle imply the statement in the proof of the Theorem $6$ above because I could not to see immediately it.
Thanks in advance!
