ISSN $18802818$

数理解析研究所講究録 1862

ライ空間の幾何学

京都大学数理解析研究所
2013 年 11 月

数理解析研究所講究録は，京都大学数理解析研究所の共同利用研究集会および共同研究の記録として 1964 年に刊行が開始されました．現在の共同利用共同研究拠点(2010 年発足) の前身である，全国共同利用研究所として当研究所が発足した翌年のことでしたが以来半世紀，毎年数十巻を刊行し，2012 年には第 1800 巻が刊行されるに至りました．第 1 巻から第 1840 巻までに収録された論文数は 26,808 編，総頁数は 317,199 頁という膨大なものであり，最先端の数学数理科学分野の研究状況を伝えるのみならず，我が国の数学数理科学の発展の歴史を留める文献として，他に類例を見ない論文集となっています．

講究録の内容は当研究所のウェブサイトおよび京都大学の学術情報リポジトリにおいても公開され，年間の総アクセス数は 1,254,383 回 (2012 年度) を数えるなど，多数の方にご利用いただいています．

講究録の使用言語は論文著者の判断に任されていますが結果的に日本語が多用されていることが特徴の一つとなっています．その結果，講究録は，数学数理科学の広い領域における最先端の専門知識に母国語でアクセスできるものとして，近年の英語化の流れの中で，重要な文献となりつつあります．

当研究所の共同利用事業に参加し講究録の論文を執筆していただいた多数の方々に対し，講究録を大きく成長させていただいたことを深く感謝いたしますとともに，これからも，当研究所の共同利用共同研究拠点としての活動にご参加いただき，講究録の発展にご協力いただけますよう心よりお願い申し上げます．

RIMS$K\hat{o}k\gamma\hat{u}rok$

1862

Geometry of Moduli Space ofLow Dimensional Manifolds
October $29\sim 31_{y}$ 2012edited by Sumio Yamada

November, 2013

Research Institute for Mathematical Sciences
Kyoto University, Kyoto, Japan
This is a report of research done at the Research Institute for Mathematical
Sciences, Kyoto University. The papers contained herein are in final form
and will not be submitted for publication elsewhere.

Geometry of Moduli Space of Low Dimensional
Manifolds
RIMS Kyoto University

October 29-31, 2012

ProgramMonday, October 29

9:50-11:20

11:30-12:30

Hideki Miyachi (Osaka Univ.)”Extremal length geometry on Teichm\"uller space”
Shohei Ma (Nagoya Univ.)“The rationality of the moduli spaces of trigonal curves”

14:00-15:00 Shinichiro Matsuo (Osaka Univ.)“Brody curves and mean dimension”
15:10-16:40 Yoshinobu Kamishima (Tokyo Metropolitan Univ.)$($

Conformally flat Lorentzian parabolic manifold”

Tuesday, October 30

9:30-11:00

11:10-12:10
13:30-15:00
15:10-16:40

Kenichi Ohshika (Osaka Univ.)“Deformation spaces of Kleinian groups and group actions”
Kunio Obitsu (Kagoshima Univ.)“Recent progress on Takhtajan-Zograf and Weil-Petersson metrics”
Gilbert Weinstein (Univ. of Alabama at Birmingham/Monash Univ.)“Mass, area, charge and angular momentumof initial data in general relativity”
Marcus Khuri (State Univ. of New York at Stony Brook)‘Quasi-local mass and the static extension problem
in general relativity”$t$

Wednesday, October 31

9:30-10:30

Asuka Takatsu (Nagoya Univ.)”Isoperimetric profile of radial probability measures”
10:40-12:10 Tetsuya Shiromzu (Kyoto Univ.)“Generalised Lichinerowicz lemma, black hole uniquenessand positive mass theorem”

低次元多様体モジュライ空間の幾何学
Geometry of Moduli Space of Low Dimensional Manifolds

RIMS 研究集会報告集

2012 年 10 月 29 日 〜10 月 31 日
研究代表者

山田

澄生 (Sumio Yamada)

目次

1. CONFORMALLY FLAT LORENTZ PARABOLIC MANIFOLD $————————1$
首都大理工学 (Tokyo Metro. U.)神島芳宣 (Yoshinobu Kamishima)$———-14$

2. THE CHARGED PENROSE INEQUALITY FOR A SPHERICALLY SYMMETRICBLACK HOLE

Vanderbilt U.
Stony Brook U.

Marcelo M. Disconzi

Marcus A. Khuri$———-$

3. THURSTON THEORY ON TEICHM\"ULLER SPACE WITH EXTREMALLENGTH

阪大理学 (Osaka $U$ .)宮地

秀樹 (Hideki Miyachi)

4. Recent progress on Takhtajan-Zograf and Weil-Petersson metrics $———————–30$
鹿児島大理 (Kagoshima $U$ .)小櫃

邦夫 (Kunio Obitsu)

5. Generalised Lichnerowicz lemma, black hole uniqueness and positive mass theorem –42京大・理学 (Kyoto $U$ .)白水徹也 (Tetsuya Shiromizu)

6. Properties of -Gaussian measures related to the isoperimetric and$q$concentration Profiles

52$———————–$

名大多元数理科学 (Nagoya$U$.)高津

飛鳥 (Asuka Takatsu)

7. ON THE RIEMANNIAN PENROSE INEQUALITY WITH CHARGE AND
THE COSMIC CENSORSHIP CONJECTURE $—————————————63$
Stony Brook U.

Marcus A. Khuri

Ariel U. Samaria

Gilbert Weinstein

学習院大理 (Gakushuin $U$ .)山田

澄生 (Sumio Yamada)講究録$K\hat{o}br\hat{u}roku$-IMS$K\hat{0}ky\hat{u}\iota \mathfrak{v}ku$

was started in 1964 as the proceedings of symposia colloquia andworkshops supported by RIMS, the Research Institute for Mathematical Sciences, Kyoto
University It was the next year of the establishment of $RmIS$ as one of the nationwide

Cooperative Research Centers, the preceding system of the current Joint Usage/ResearchCenters that started in 2010. For half a century since then, about 50 to 60 volumes have been
issued each year, and the 1, $800th$ volume was issued in 2012. The volumes
from$ofK\hat{o}1q^{r}\hat{u}roku$

the lst through the 1, $840th$, containing enormous 26,808 articles and 317,199 pages, not only
deliver the latest research activities in mathematics and mathematical sciences but alsovaluable and incomparable collections of articles that pass down history of progress$\infty nstitut\epsilon$of mathematics and mathematical science in Japan.

are available on the websites of RIMS and Kyoto University ResearchInformation Repository They are very frequently accessed on the internet, with a total of as
Articles in$K\hat{o}ky\hat{u}\iota oku$

many as 1,254,383 accesses in 2012.
The authors choose the languages to write articles, and many are written in Japanese, which
is one of the characteristics of. As a result,is regarded as a significant
and important literature which allows easy access to the latest speciahzed knowledge in the$K\hat{0}br\hat{u}roku$$K\hat{o}br\hat{u}roku$

large fields of mathematics and mathematical scienoes written in native language $f0r$ Japanesereaders, while more and more research papers are being written in English in recent years.

We are deeply grateful to many of those who have participated in rperative research
your continuousactivities of RIMS and greatly developed. We heartily ask
participation in research activities at RIMS as a Joint Usage Research Center and your warm$\alpha$$K\hat{0}ky\hat{u}1\mathfrak{v}ku$

support and cooperation $fOr$ the fruitful development ofK\^obr\^uroku.

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