2001 Fiscal Year Final Research Report Summary
Morse index and heat kernel of constant mean curvature surfaces
| Project/Area Number |
11640077
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kobe University |
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Principal Investigator |
WATANABE Kiyoshi Kobe University, Faculty of Science, Associate Professor, 理学部, 助教授 (60091245)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Koutaro KYUSYU University, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (10221657)
ROSSMAN Wayne Kobe University, Faculty of Science, Associate Professor, 理学部, 助教授 (50284485)
MIYAKAWA Teturo Kobe University, Faculty of Science, Professor, 理学部, 教授 (10033929)
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| Project Period (FY) |
1999 – 2001
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| Keywords | constant mean curvature / ends / heat kernel / Morse Index / Wente tori / minimal surface / Delaumay surface / Gauss map |
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| Research Abstract |
1. The Morse Index of Wente Tori
We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planer principal curves. We then prove a result that gives an algorithm for computing the index sharply.
2. Doubly Perodic Minimal Surfaces
We consider the question of existence of embedded doubly periodic minimal surfaces with Scherk-type ends. We extend the existance results of Karcher and Wei to more cases and we find other cases where existance dose not hold.
3. Embeddedness of area-minimizing disks
We show that a polygonal Jordan cave C satisfies certain conditions, then the least-area Douglas-Rado disk with boundary C is unique and is a smooth graph. With our result we can apply this method to a wider range of complete catenoid-ended minimal surfaces.
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Research Products
(11 results)
