Resumen de A necessary condition for weak maximum modulus sets of 2-analytic functions

Abtin Daghighi

• Let ?⊂ℂ be a domain and let ?(?)=?(?)+?¯?(?), where a, b are holomorphic for ?∈?. Denote by ? the set of points in ? at which |?| attains weak local maximum and denote by ? the set of points in ? at which |?| attains strict local maximum. We prove that for each ?∈?∖? , |?(?)|=∣∣∣(∂?∂?+?¯∂?∂?)(?)∣∣∣ Furthermore, if there is a real analytic curve ?:?→?∖? (where I is an open real interval), if a, b are complex polynomials, and if ?∘? has a complex polynomial extension, then either f is constant or ? has constant curvature.