• 主講人

Jiaping Wang 王嘉平 (University of Minnesota)

Prof. Marcello Lucia (NCTS)

Prof. Dong-Ho Tsai 蔡東和 (NTHU)

Prof. Shun-Cheng Chang 張樹城 (NTHU)

Prof. Chiung-Jue Sung 宋瓊珠 (NCCU)

2005年秋季，每星期一，上午 10:30-12:00//下午 1:30-3:00

第一次上課時間: 九月十九日開始

詳細的課程進度 請參考Course Schedule

新竹市清華大學綜合三館四樓

國家理論科學研究中心數學組 Lecture Room B

• 預備知識

1.The course will be more or less self-contained with minimal prerequisite.

2.Some knowledge in geometry and PDE will be helpful, but not necessary.

++王嘉平 教授: The classical de Rham-Hodge theory, which relates the cohomology group of a compact manifold to its space of harmonic forms, is one of the most fundamental theories in modern mathematics. With the help of an analysis technique first introduced by Bochner (called Bochner technique), the theory has yielded many interesting and important results relating topology to geometry. Even though the theory is no longer valid on noncompact manifolds, the idea of using analysis to understand the interaction between topology and geometry is pivotal and fruitful in geometric analysis. In this introductory course, we will explain some results along this line. Particular emphasis will be on the application of function theory to both geometry and topology. A partial list includes Cheeger-Gromoll splitting theorem, the classification of stable minimal surfaces and the recently discovered rigidity phenomena concerning manifolds with maximal bottom spectrum.

++Marcello Lucia 教授: (1) Introduce some elements of functional analysis, and explain how to use it for getting solutions of linear PDE. (2) Variational methods. (3) Isoperimetric inequality and coarea formula. (4) Study the nonlinear problem \Delta+ e^u = C on a two    dimensional manifold.

++蔡東和 教授: We shall study curvature flows of plane curves and their geometric properties. In particular, we shall focus on the contents of the following two papers: [1] . S. Angenent, On the formation of singularities in the curve shortening flow, J. Diff. Geom., 33 (1991), 601-633. [2] . M.  Gage and R. Hamilton, The heat equation shrinking convex plane curves, J. Diff. Geom., 23 (1986), 69-96.
　

張樹城 教授: TBA

宋瓊珠 教授: TBA

• 課程聯絡人

 dhtsai@math.nthu.edu.tw

 TEL: 03-5745131#3062