The Gauss images of complete minimal surfaces of genus zero of finite total curvature
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909241898434560 |
|---|---|
| author | Kawakami, Yu Watanabe, Mototsugu |
| author_facet | Kawakami, Yu Watanabe, Mototsugu |
| contents | This paper aims to present a systematic study on the Gauss images of complete minimal surfaces of genus 0 of finite total curvature in Euclidean 3-space and Euclidean 4-space. We focus on the number of omitted values and the total weight of the totally ramified values of their Gauss maps. In particular, we construct new complete minimal surfaces of finite total curvature whose Gauss maps have 2 omitted values and 1 totally ramified value of order 2, that is, the total weight of the totally ramified values of their Gauss maps are 5/2 (=2.5) in Euclidean 3-space and Euclidean 4-space, respectively. Moreover we discuss several outstanding problems in this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Gauss images of complete minimal surfaces of genus zero of finite total curvature Kawakami, Yu Watanabe, Mototsugu Differential Geometry Complex Variables 53A10, 30D35, 53A05 This paper aims to present a systematic study on the Gauss images of complete minimal surfaces of genus 0 of finite total curvature in Euclidean 3-space and Euclidean 4-space. We focus on the number of omitted values and the total weight of the totally ramified values of their Gauss maps. In particular, we construct new complete minimal surfaces of finite total curvature whose Gauss maps have 2 omitted values and 1 totally ramified value of order 2, that is, the total weight of the totally ramified values of their Gauss maps are 5/2 (=2.5) in Euclidean 3-space and Euclidean 4-space, respectively. Moreover we discuss several outstanding problems in this study. |
| title | The Gauss images of complete minimal surfaces of genus zero of finite total curvature |
| topic | Differential Geometry Complex Variables 53A10, 30D35, 53A05 |
| url | https://arxiv.org/abs/2309.06846 |