Uniqueness of minimal surfaces, Jacobi fields,and flat structures

Author:

Lee Hojoo

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference28 articles.

1. W. Blaschke, Einfiihrung in die Differentialgeometrie, Springer, Berlin, 1950.

2. University of Kansas, Department of Mathematics Technical Report 19 (New Series);Chern, S. S.,1968

3. Simple proofs of two theorems on minimal surfaces;Chern, Shiing-shen;Enseign. Math. (2),1969

4. Isoperimetric inequality for flat surfaces;Choe, Jaigyoung,2009

5. Stable complete minimal surfaces in 𝑅³ are planes;do Carmo, M.;Bull. Amer. Math. Soc. (N.S.),1979

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3