Hi there

i need some help with this question

let D=D(0,1),let u be a continuous function on (\bar{D}) that is subharmonic on D,and let E={z \in \bar{D} :u(z)\leqslant 0}

Explain why C\E is connected,

and let u be subharmonic function on the strip U={z in C : -1< Im z < 1}

such that

lim sup u(z)\v(z)\leqslant 0 (w \in \partial \infty U)

where v(x+iy)=coshx cosy

show that u\leqslant 0

thanks (Nerd)