回首頁

回第28期

滕楚蓮在幾何學上的貢獻


本文預覽

作       者 烏蘭貝克(Karen Uhlenbeck)

作者簡介 烏蘭貝克是現代幾何分析的創始人之一,她是 德州大學奧斯汀分校數學榮譽教授,曾擔任該校的Sid W. Richardson 講座教席,現在在普林斯頓高等研究院訪問。她是自2003 年設立阿貝爾獎以來第一位、也是迄今為止唯一一位於2019 年獲獎的女性。她將一半的獎金捐給了那些致力於鼓勵促進女性更多參與數學研究的組織。

譯      者 翁秉仁

譯者簡介 翁秉仁為臺灣大學數學系副教授。

本文出處    本文譯自Karen Uhlenbeck,“The Contributions of Chuu-Lian Terng to Geometry”, Notices of the AMS 71(2024)No. 3, AMS。� American Mathematical Society 2008. All rights reserved。感謝AMS 與作者同意轉載翻譯。

延伸閱讀

參考資料

[AvdL03] Kh. Aratin and Zh. van de Ler, An integrable structure based on the WDVV equations (Russian, with Russian summary), Teoret. Mat. Fiz. 134 (2003), no. 1, 18–31, DOI 10.1023/A:1021859421126; English transl., Theoret. And Math. Phys. 134 (2003), no. 1, 14–26.   MR2021727

[CT80] Shiing Shen Chern and Chuu Lian Terng, An analogue of Bäcklund’s theorem in affine geometry,   Rocky Mountain J. Math. 10 (1980), no. 1, 105–124, DOI 10.1216/RMJ-1980-10-1-105. MR573866

[Czu10] Magdalena Czubak, Local wellposedness for the 2 + 1-dimensional monopole equation, Anal. PDE   3 (2010), no. 2, 151–174, DOI 10.2140/apde.2010.3.151. MR2657452

[DT07] Bo Dai and Chuu-Lian Terng, Bäcklund transformations, Ward solitons, and unitons, J. Differential Geom. 75 (2007), no. 1, 57–108. MR2282725

[DTU06] Bo Dai, Chuu-Lian Terng, and Karen Uhlenbeck, On the space-time monopole equation, Surveys in differential geometry. Vol. X, Surv. Differ. Geom., vol. 10, Int. Press, Somerville, MA, 2006, pp. 1–30, DOI 10.4310/SDG.2005.v10.n1.a1. MR2408220

[Dei19] Percy Deift, Riemann-Hilbert problems, Random matrices, IAS/Park City Math. Ser., vol. 26, Amer. Math. Soc., Providence, RI, 2019, pp. 1–40. MR3971152

[DZ02] Percy Deift and Xin Zhou, A priori 𝐿𝑝-estimates for solutions of Riemann-Hilbert problems, Int. Math. Res. Not. 40 (2002), 2121–2154, DOI 10.1155/S1073792802205103. MR1930757

[DdS84] V. G. Drinfeld and V. V. Sokolov, Lie algebras and equations of Korteweg-de Vries type (Russian), Current problems in mathematics, Vol. 24, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, pp. 81–180. MR760998

[HY18] Hyungjin Huh and Jihyun Yim, The Cauchy problem for space-time monopole equations in Sobolev spaces, J. Math. Phys. 59 (2018), no. 4, 043510, 10, DOI 10.1063/1.5022866. MR3794037

[MNPS19] Dana Mendelson, Andrea R. Nahmod, Nataˇsa Pavlovi´c, and Gigliola Staffilani, An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on , Trans. Amer. Math. Soc.  371 (2019), no. 7, 5179–5202, DOI 10.1090/tran/7726. MR3934481

[PT88] Richard S. Palais and Chuu-Lian Terng, Critical point theory and submanifold geometry, Lecture Notes in Mathematics, vol. 1353, Springer-Verlag, Berlin, 1988, DOI 10.1007/BFb0087442. MR972503

[SW85] Graeme Segal and George Wilson, Loop groups and equations of KdV type, Inst. Hautes E´ tudes Sci. Publ. Math. 61 (1985), 5–65. MR783348

[Ter97] Chuu-Lian Terng, Soliton equations and differential geometry, J. Differential Geom. 45 (1997), no. 2, 407–445. MR1449979

[TU00] Chuu-Lian Terng and Karen Uhlenbeck, Geometry of solitons, Notices Amer. Math. Soc. 47 (2000), no. 1, 17–25. MR1733063

[TU06] Chuu-Lian Terng and Karen Uhlenbeck, Schrödinger flows on Grassmannians, Integrable systems, geometry, and topology, AMS/IP Stud. Adv. Math., vol. 36, Amer. Math. Soc., Providence, RI, 2006,  pp. 235–256, DOI 10.1090/amsip/036/06. MR2222517

[TU11] Chuu-Lian Terng and Karen Uhlenbeck, The 𝑛×𝑛 KdV hierarchy, J. Fixed Point Theory Appl. 10 (2011), no. 1, 37–61, DOI 10.1007/s11784-011-0056-x. MR2825739

[TU16] Chuu-Lian Terng and Karen Uhlenbeck, Tau functions and Virasoro actions for soliton hierarchies, Comm. Math. Phys. 342 (2016), no. 1, 117–150, DOI 10.1007/s00220-015-2562-y. MR3455147

[TZ19] Chuu-Lian Terng and Zhiwei Wu, 𝑛-dimension central affine curve flows, J. Differential Geom. 111 (2019), no. 1, 145–189, DOI 10.4310/jdg/1547607689. MR3909906

[Ter22] Chuu-Lian Terng, Reflections of Chuu-Lian Terng, AWM’s twelfth president, Fifty years of women In mathematics—reminiscences, history, and visions for the future of AWM, Assoc. Women Math. Ser., vol. 28, Springer, Cham, [2022] ©2022, pp. 673–677, DOI 10.1007/978-3-030-82658-1_60. MR4454659

[Th00] Gudlaugur Thorbergsson, A survey on isoparametric hypersurfaces and their generalizations, Handbook of differential geometry, Vol. I, North-Holland, Amsterdam, 2000, pp. 963–995, DOI 10.1016/S1874-5741(00)80013-8. MR1736861