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Proceedings of the American Mathematical Society

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Uniqueness of minimal surfaces, Jacobi fields,and flat structures


Author: Hojoo Lee
Journal: Proc. Amer. Math. Soc. 148 (2020), 3059-3071
MSC (2010): Primary 53A10, 49Q05
DOI: https://doi.org/10.1090/proc/14941
Published electronically: March 18, 2020
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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.


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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
Email: kiarostami@jbnu.ac.kr \textrm{and} compactkoala@gmail.com

DOI: https://doi.org/10.1090/proc/14941
Keywords: Flat structures, harmonic functions, Jacobi fields, minimal surfaces, Scherk's surface
Received by editor(s): December 11, 2018
Received by editor(s) in revised form: October 5, 2019
Published electronically: March 18, 2020
Dedicated: Dedicated to Jaigyoung Choe on the occasion of his $65$th birthday.
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2020 American Mathematical Society