1990 Fiscal Year Final Research Report Summary
Potential Theory and its Applications
| Project/Area Number |
01540103
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Chiba University |
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Principal Investigator |
YOSHIDA Hidenobu Chiba Univ. Dept. Math. Professor, 理学部, 教授 (60009280)
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| Co-Investigator(Kenkyū-buntansha) |
NAGISA Masaru Chiba Univ. Dept. Math., Associate, 理学部, 助教授 (50189172)
SUGIYAMA Ken-ichi Chiba Univ. Dept. Math., Associate, 理学部, 助教授 (90206441)
KOSHITANI Sigeo Chiba Univ. Dept. Math., Associate Profes, 理学部, 助教授 (30125926)
YANAGIHARA Niro Chiba Univ. Dept. Math., Professor, 理学部, 教授 (70009041)
TAKAGI Ryoichi Chiba Univ. Dept. Math., Professor, 理学部, 教授 (00015562)
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| Project Period (FY) |
1989 – 1990
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| Keywords | least harmonic majorant / Dirichlet Problem / Einstein-Kahler metric / Bogomolov-Gieseker type inequality / Chern class / Sylow p-subgroup / p-block of a finite Group / 01Theorem of Phragmen-Lindelof type |
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| Research Abstract |
1. For a subharmonic function u defined on a cone or on a cylinder which is dominated on the boundary by a certain function, we generalize the classical Phragmen-Lindelof theorem by making a harmonic majorant of u and show that if u is non-negative in addition, our harmonic majorant is the least harmonic majorant. As an application, we gave a result concerning the classical Dirichlet problem on a cone or on a cylinder-with an unbounded function defined on the boundary.
2. Solving a degenerate Monge-Ampere equation, we shall construct a family of Einstein-Kahler metrics on the smooth part of minimal varieties of general type. We shall show a subsequence of this family of Einstein-Kahler metrics converges to an Einstein-Kahler metric, whose cohomology class corresponds properly to a negative constant multiple of the first Chern class of the variety. An inequality between Chern numbers for minimal varieties, so called Bogomolov-Gieseker type inequality, will be proved. We shall obtain a sufficient condition for the tangent sheave of certain varieties to be stable.
3. Isaacs and Smith gave several character-theoretic characterizations of finite p-solvable groups G with p-length one. They gave four equivalent conditions for a finite group G with a Sylow p-subgroup P. We generalized this to an arbitrary p-block B of a finite group G in our previous paper. The purpose of this note is to complement this.
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