TITLE: Zero sets of harmonic fucntions
QUESTION [6 upvotes]: Can a two variable Harmonic function f(x,y) be zero on a curve with a cusp?

REPLY [3 votes]: There exists an honor thesis dedicated to exactly this problem, and its generalizations: Problems in Harmonic Function Theory Ronald A. Walker, see http://scholarship.richmond.edu/cgi/viewcontent.cgi?article=1488&context=honors-theses