1998 Fiscal Year Final Research Report Summary
Analysis on Riemann surfaces and manifolds to gether with contributions to physics and engineeing
| Project/Area Number |
09640193
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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 |
解析学
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| Research Institution | Hiroshima University |
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Principal Investigator |
SHIBA Masakazu Faculty of Engineering, Hiroshima University Prof., 工学部, 教授 (70025469)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Manabu Faculty of Engineering Assoc.Prof., 工学部, 助教授 (90178773)
OHTA Yasuhiro Faculty of Engineering Res.Assist., 工学部, 助手 (10213745)
IWASE Kosei Faculty of Engineering Prof., 工学部, 教授 (10103079)
ITO Masaaki Faculty of Engineering Assoc.Prof., 工学部, 助教授 (10116535)
AIZAWA Kunio Faculty of Engineering Assoc.Prof., 工学部, 助教授 (80150895)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Riemann surfaces / Ideal fluid flow / Conformal mapping / Energy integral / Univalent functions / Potential flow / Rankine ovoids / Analytic functions |
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| Research Abstract |
We used the function-theoretic methods to obtain a new insight into the various fluid-dynamical phenomena on surfaces and manifolds. Specifically, we have been interested in Rankine ovoids on plane and Riemann surfaces. We use the function-theoretic technique (initiated by the head investigator) to study the phenomenon physically as well as mathematically. The physical investigation is based on the notions of sink and source, vortex, energy, moment and so on, while the mathematical investigation is based on our own results which have been so far obtained. Of the most importance among them is the study of compact Riemann surfaces into which a prescribed noncompact Riemann surface can be conformally embedded. We have proved that any Rankine ovoid can be realized by a univalent meromorphic function on a simply connected plane domain and that the area of the Rankine ovoid is surprisingly close to the possible maximum area which will be attained in a certain family of competing functions. The result was announced at the International Conference "Computational Methods and Function Theory (CMFT'97)" held in Nicosia, Cyprus, and will be included in the Proceedings.
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