課程說明(Course Description)：
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<br>本課程為幾何分析基礎入門課程,課程內容為簡介基本的&#63972;&#63809;與應用。
<br>期望幫助同學在幾何相關領域的學習,帶&#63924;學生研&#63834;幾何分析的重要問題、&#63972;&#63809;與其應用。
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<br>This course is an introduction to the study of Riemannian geometry via the methods of calculus and differential equations. It includes both the use of geometrical methods in the study of partial differential equations and the application of the theory of partial differential equations to geometry. We study the Maximum Principles, Liouville Theorem for Harmonic functions, Bishop-Gromov Volume Comparison Theorem, Bochner formulas, Harnack Estimate for the Heat equation, Ricci Solitons, and Harmonic forms on Riemannian Manifolds. 
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<br>References:
<br>S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Universitext, Springer.
<br>T. Sakaio, Riemannian Geometry, AMS.
<br>P. Li: Geometric Analysis, Cambridge studies in advanced mathematics, vol. 134, 2012
<br>Warner: Foundations of Differential Manifolds and Lie Groups. 
<br>Do Carmo: Riemannian Geometry. 
<br>Jost: Riemannian Geometry and Geometric Analysis.  
<br>L. Evans: Partial Differential Equaitons
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<br>Course score =Oral presentation and Homework.
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