2018/12/04 by Hojoo Lee, Lee, Hojoo
Mathematics · #49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:49Q05 #msc:53A10
paper · pdf · doi:10.48550/arxiv.1812.01401
typos corrected, comments welcome
arxiv created 2019/05/31 · arxiv updated 2019/06/03
Inspired by the Finn-Osserman (1964), Chern (1969), do Carmo-Peng (1979) proofs of the Bernstein theorem, which characterizes flat planes as the only entire minimal graphs, we prove a new rigidity theorem for associate families connecting the doubly periodic Scherk graphs and the singly periodic Scherk towers. Our characterization of Scherk's surfaces discovers a new idea from the original Finn-Osserman curvature estimate. Combining two generically independent flat structures introduced by Chern and Ricci, we shall construct geometric harmonic functions on minimal surfaces, and establish that periodic minimal surfaces admit fresh uniqueness results.