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課程名稱 |
幾何分析專題
Topics in Geometry Analysis |
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開課學期 |
102-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
張樹城 |
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課號 |
MATH8316 |
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課程識別碼 |
221 U5090 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五7,8,9(14:20~17:20) |
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上課地點 |
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備註 |
上課教室：數學研究中心(新數學館103教室)。
總人數上限：10人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Contents of the Lecture :
1 First and Second Variational Formulas for Area
2 Comparison Theorems
3 Bochner-Weitzenbock Formulas
4 Laplacian Comparison Theorem
5 Poincare Inequality and the First Eigenvalue
6 Gradient Estimate and Harnack Inequality
7 Isoperimetric Inequalities and Sobolev Inequalities
8 Gradient Estimate and Harnack Inequality for the Heat Equation
9 Stability of Minimal Hypersurfaces in a Manifold |
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課程目標 |
The main goal of this lecture is to present the basic tools that are necessary for research in geometric analysis. The main theme centers around linear theory, such as the Laplace equation, the heat equation. The methods in dealing with these problems are quite often useful to the study of nonlinear partial differential equations that arise in geometry. |
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課程要求 |
Report on related papers |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
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參考書目 |
P. Li, Lecture on Geometric Analysis, 2012 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
report on paper |
100% |
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