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幾何学分科会の皆様， </div>
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<div dir="ltr">Workshop 「Geometric Analysis in Geometry and Topology 2017」（第2報）</div>
を下記の要領で開催いたしますのでご案内申し上げます．<br>
なお案内のPDF-file（日本語版，英語版）とも，<br>
幾何学分科会のwebページに最新のものがをおいてあります．<br>
<br>
<div dir="ltr">多数のご参加をお待ち申し上げます．</div>
<div dir="ltr">またお近くの方にお声をかけて頂ければ幸いです．</div>
<div dir="ltr"> </div>
<div dir="ltr">芥川和雄<br>
<br>
<br>
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\title{Workshop\\ </p>
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\quad \\ </p>
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Geometric Analysis in Geometry and Topology 2017}</p>
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%\date{2015/06/8}</p>
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%\author{Kazuo Akutagawa}</p>
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\begin{document}</p>
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\maketitle</p>
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{\bf Workshop 「Geometric Analysis in Geometry and Topology 2017」\\ </p>
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\quad \\ </p>
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\qquad \qquad を下記の要領で開催いたしますのでご案内申し上げます．\\ </p>
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\quad \\ </p>
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\qquad \qquad \qquad \qquad \qquad \qquad \quad {\bf 記}\\ </p>
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\quad \\ </p>
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{\bf 日時}：12月19日（火）〜12月22日（金）・・・4日間\\ </p>
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{\bf 場所}：東京理科大学（神楽坂），森戸記念館\\</p>
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\quad \\ </p>
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\quad \\ </p>
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{\bf 講演者予定者}：\\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・{\bf 納谷 信 (名古屋大学・多元数理)}\\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・{\bf 本多 正平 (東北大学・理)}\\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・{\bf 松尾 信一郎 (名古屋大学・多元数理)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・{\bf 松本 佳彦 (大阪大学・理)}\\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf スケジュール}\\ </p>
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・・・・・・・・・・・ 10:00--11:00\qquad 11:30--12:30\qquad 14:00--15:00\qquad 15:30--16:30\\</p>
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{\bf Dec.\,19}\qquad 本多-1\qquad \qquad \quad 松本-1\qquad \qquad \quad 本多-2\qquad\qquad 松本-2\\</p>
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{\bf Dec.\,20}\qquad 本多-3\qquad \qquad \quad 松本-3\qquad \qquad \quad 本多-4\qquad\qquad 松本-4\\</p>
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{\bf Dec.\,21}\qquad 松尾-1\qquad \qquad \quad 納谷-1\qquad \qquad \quad 松尾-2\qquad\qquad 納谷-2\\
</p>
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{\bf Dec.\,22}\qquad 松尾-3\qquad \qquad \quad 納谷-3\qquad \qquad \quad 松尾-4\qquad\qquad 納谷-4\\
</p>
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\quad \\ </p>
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\quad \\ </p>
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{\bf 組織員}：\\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・小池直之（東京理科大学・理）\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・中村 周(東京大学・数理)\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・古田幹雄(東京大学・数理)\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・松尾信一郎(名古屋大学・多元)\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・小林 治(前 大阪大学・理)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・松本佳彦(大阪大学・理)\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・Rafe Mazzeo (Stanford University, Foreign adviser)\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・芥川和雄(東京工業大学・理学院)\\</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・高木章子(担当事務：東京工業大学・理学院)\\ </p>
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%-----------------------------------------------\\ </p>
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%\quad\\ </p>
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%{\bf 関連する研究会}\\</p>
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%The First Japan-Taiwan Joint Conference on Differential Geometry $\&$</p>
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%the 8th TIMS-OCAMI-WASEDA Joint International Workshop on Differential Geometry and Geometric Analysis\\
</p>
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%\quad \\ </p>
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%Waseda University, Japan, December 13th-17th 2016 (Tuesday-Saturday).\\ </p>
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%\quad \\ </p>
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%<a class="moz-txt-link-freetext" href="https://sites.google.com/site/jtgeometryconference/">https://sites.google.com/site/jtgeometryconference/</a></p>
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%\quad \\ ---------------------------------------------------------------------------------------\\
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\newpage\noindent</p>
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\underline{\bf 講演タイトル・講演要旨}\\ </p>
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\quad \\ </p>
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$\bullet$\ \ {\bf 納谷 信 (名古屋大学・多元数理)}\\ </p>
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\quad \\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Hersch-Yang-Yauの不等式と第1固有値の最大化について} \\ </p>
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<br>
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この連続講演では，閉曲面においてラプラシアンの第１固有値を（面積一定の仮定の下で）最大化する計量について，最近の進展を中心に解説する．</p>
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第１回では，そのような問題の出発点となったHersch-Yang-Yauの不等式（1970, 1980）を証明とともに紹介する．</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
これは第１固有値（と面積の積）が曲面の種数のみに依存する定数で上から押さえられることを示す不等式である．</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
第２回では，最大化計量の存在問題に関する最近の進展について，球面内の極小曲面との関わりを交えて概説する．</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
第3回では，種数２の場合に最大化計量を明示的に予言するJacobson-Levitin-Nadirashvili-Nigam-Polterovich予想とその肯定的解決（庄田敏宏氏との共同研究）について述べさせていただく．</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
そして，第４回では最大化計量の存在定理およびそのような計量が球面への極小はめ込みによる誘導計量として与えられるという事実に対して説明を与える． \\ </p>
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\quad \\ </p>
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\quad \\ </p>
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$\bullet$\ \ {\bf 本多 正平 (東北大学・理)}\\ </p>
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\quad \\ </p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf 熱流とRicci曲率} \\ </p>
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<br>
</p>
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関数を良い関数で近似する，という問題を考える．この問を真剣に考えると，考えている空間のRicci曲率が見えてくる．</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
この観察は最近のRicci曲率に関わる特異空間の解析の急速な発展を支えており，熱流がキーワードである．</p>
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margin-right:0px; -qt-block-indent:0; text-indent:0px;">
この熱流とRicci曲率とその応用（特にGromov-Hausdorff収束理論への応用）を解説する． \\ </p>
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\quad \\ </p>
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\quad \\ </p>
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$\bullet$\ \ {\bf 松尾 信一郎 (名古屋大・多元数理)}\\ </p>
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\quad \\ </p>
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\underline{\bf 高次元ゲージ理論入門}\\ </p>
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<br>
</p>
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最近静かな盛り上がりを見せつつある高次元ゲージ理論について，</p>
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その幾何解析的側面を中心に解説する．\\ </p>
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\quad \\ </p>
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\quad \\ </p>
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$\bullet$\ \ {\bf 松本 佳彦 (大阪大学・理)}\\ </p>
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\underline{\bf Poincar\'e-Einstein計量の基礎と展開}\\ </p>
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$\overline{X}$を$n+1$次元のコンパクトな境界付き多様体とする．</p>
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その内部$X$で定義されたRiemann計量$g$は，</p>
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次の2つの性質を持つときPoincar\'e--Einstein計量（または共形コンパクトEinstein計量）であると言われる．</p>
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\begin{enumerate}</p>
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\item[(i)]</p>
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境界定義関数$\rho\in C^\infty(\overline{X})$を任意に選んで$\overline{g}=\rho^2g$とおくと，</p>
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$\overline{g}$は境界まで非退化に拡張される（状況に応じて適切に境界正則性の条件を課す）．</p>
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\item[(ii)]</p>
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$g$はEinstein方程式${\rm Ric}(g)=-ng$を満たす．</p>
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\end{enumerate}</p>
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最も基本的な例は，$\mathbb{R}^{n+1}$の単位開球のPoincar\'e計量である．</p>
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本講演ではPoincar\'e--Einstein計量の存在問題に関連する諸結果を解説する．</p>
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単位開球のPoincar\'e計量を変形できることを示すGraham--Leeの定理(1991)について丁寧に述べ，</p>
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さらに一意性の不成立や非存在に関するAnderson (2003)，Gursky--Han (2017)の結果を扱う予定である．</p>
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\end{document}<br>
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