Uniqueness of minimal surfaces, Jacobi fields,and flat structures

Lee, Hojoo

doi:10.1090/proc/14941

Uniqueness of minimal surfaces, Jacobi fields,and flat structures
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Proc. Amer. Math. Soc. 148 (2020), 3059-3071 Request permission

Abstract:

Combining two generically independent flat structures introduced by Chern and Ricci, we construct geometric harmonic functions on minimal surfaces. We show that various periodic minimal surfaces admit new uniqueness results in terms of our geometric harmonic functions. We prove a new rigidity theorem for associate families connecting the doubly periodic Scherk graphs and the singly periodic Scherk towers.

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