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$C^1$-umbilics with
arbitrarily high indices
Naoya Ando, Toshifumi Fujiyama and Masaaki Umehara |
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Vol. 288 (2017), No. 1, 1–26
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Abstract |
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We show that -umbilics with arbitrarily high indices exist. This implies that more than -regularity is required to prove Loewner’s conjecture. |
Keywords
umbilic, curvature line, Carathéodory's conjecture,
Loewner's conjecture
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Mathematical Subject Classification 2010
Primary: 53A05, 53C45
Secondary: 57R42, 37C10, 53A30
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Milestones
Received: 7 August 2015
Revised: 25 September 2016
Accepted: 26 September 2016
Published: 8 April 2017
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Authors |
| Naoya Ando | |
| Graduate School of Science and
Technology Kumamoto University 2-39-1 Kurokami Kumamoto 860-8555 Japan |
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| Toshifumi Fujiyama | |
| Department of Mathematical
Informatics Graduate School of Information Science and Technology University of Tokyo Tokyo 113-8656 Japan |
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| Masaaki Umehara | |
| Department of Mathematical and
Computing Sciences Tokyo Institute of Technology 2-12-1-W8-34, O-okayama Meguro-ku Tokyo 152-8552 Japan |
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