Singularities and balancing conditions on the theory of minimal surfaces and related geometric variational problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540232
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Osaka City University
• Principal Investigator: KATO Shin 大阪市立大学, 大学院理学研究科, 准教授 (10243354)
• Co-Investigator(Kenkyū-buntansha): TAKAHASHI Futoshi 大阪市立大学, 大学院理学研究科, 教授 (10374901) ; KOMORI Yohei 早稲田大学, 教育学部, 教授 (70264794)
• Co-Investigator(Renkei-kenkyūsha): KASUE Atsushi 金沢大学, 理工学研究域数物科学系, 教授 (40152657)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 多様体上の解析 / 極小曲面

Outline of Final Research Achievements

We formulated the condition for the existence of n-noids of genus 1 in the Euclidian 3-space whose complete system of representatives of poles of Gauss map and that of ends coincide with each other. Moreover, we constructed new examples of such n-noids. We also decided the indices and nullities of n-noids of genes 0 under the condition that n is 4, or n is greater than 4 and the n-noid is symmetric in a sense. Moreover, we got a result on the relation between flux and nullity of n-noids.　We also constructed a 1-parameter family of n-noids defined on punctured projective planes under the condition that n is an even number greater than or equal to 4, and that all of the ends of the surface is catenoidal type. It should be remarked here that only known examples of n-noids defined on punctured projective planes have odd number of planer ends.

Free Research Field

微分幾何学