MathDB

Let

e_1,\ldots, e_n

be semilines on the plane starting from a common point. Prove that if there is no

u\not\equiv 0

harmonic function on the whole plane that vanishes on the set

e_1\cup \cdots \cup e_n

, then there exists a pair

i,j

of indices such that no

u\not\equiv 0

harmonic function on the whole plane exists that vanishes on

e_i\cup e_j

Problem Statement