本課程為幾何分析導論課程,課程內容為簡介基本的幾何分析知識與應用。
<br>期望幫助同學在幾何相關領域的學習,帶領學生研讀幾何分析的重要問題與其應用.
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<br>This course is for the study of Riemannian geometry via the methods of calculus 
<br>and differential equations. It includes using geometrical forms to analyze 
<br>partial differential equations and applying the theory of partial differential 
<br>equations to geometry. 
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<br>* Laplacian and Volume Comparison Theorems  
<br>* Harmonic functions, Green's functions
<br>* Splitting Theorem 
<br>* Gradient Estimate and Harnack Inequality 
<br>* Manifolds with Positive Spectrum   
<br>* Stable Minimal Surfaces in a 3-Manifold 
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<br>References:
<br>Jurgen Jost, Riemannian Geometry and Geometric Analysis, Springer 2011.
<br>Peter Li, Geometric Analysis, Cambridge Univ. Press 2012. 
<br>Peter Petersen, Riemannian Geometry, Springer 2006.
<br>F. John: Partial Differential Equations. 4th Edition. 
<br>L. Evans: Partial Differential Equations
<br>Warner: Foundations of Differential Manifolds and Lie Groups. 
<br>Do Carmo: Riemannian Geometry. 
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<br>Evaluation: 
<br>Homework and Oral presentation(or Exam)(to be scheduled) 
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