## Uniqueness of minimal surfaces, Jacobi fields,and flat structures

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## 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.## References

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## Additional Information

**Hojoo Lee**- Affiliation: Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju 54896, Korea
- MR Author ID: 692348
- Email: kiarostami@jbnu.ac.kr \textrm{and} compactkoala@gmail.com
- Received by editor(s): December 11, 2018
- Received by editor(s) in revised form: October 5, 2019
- Published electronically: March 18, 2020
- Communicated by: Jia-Ping Wang
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 3059-3071 - MSC (2010): Primary 53A10, 49Q05
- DOI: https://doi.org/10.1090/proc/14941
- MathSciNet review: 4099792

Dedicated: Dedicated to Jaigyoung Choe on the occasion of his $65$th birthday.