Subharmonic Functions and The Heat Equation on Riemannian Manifolds
碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 97 === We introduce Gradient Estimate and Harnack Inequality , that are essential to the study of harmonic functions . Next we apply Poincare and mean value inequality to study some properties of harmonic and subharmonic functions on Riemannian manifold . In Chapter...
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ndltd-TW-097NCKU55070132016-05-04T04:26:10Z http://ndltd.ncl.edu.tw/handle/42267739778592325918 Subharmonic Functions and The Heat Equation on Riemannian Manifolds 黎曼流形上的半調和函數和熱方程式 Shyh-Yu Lee 李諭 碩士 國立成功大學 數學系應用數學碩博士班 97 We introduce Gradient Estimate and Harnack Inequality , that are essential to the study of harmonic functions . Next we apply Poincare and mean value inequality to study some properties of harmonic and subharmonic functions on Riemannian manifold . In Chapter 3 , we show the uniqueness properties for L^{1} solutions of the Laplace equation and the heat kernel equation . Finally , assume that manifold M with nonnegative Ricci curvature and maximal volume growth , then we discuss the behavior of the Green function and estimate the heat kernel . Kwan-Hang Lam 林君�� 學位論文 ; thesis 66 en_US |
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NDLTD |
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en_US |
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Others
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NDLTD |
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碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 97 === We introduce Gradient Estimate and Harnack Inequality , that are essential to the study of harmonic functions . Next we apply Poincare and mean value inequality to study some properties of
harmonic and subharmonic functions on Riemannian manifold . In Chapter 3 , we show the uniqueness properties for L^{1} solutions of the Laplace equation and the heat kernel equation .
Finally , assume that manifold M with nonnegative Ricci curvature and maximal volume growth , then we discuss the behavior of the Green function and estimate the heat kernel .
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| author2 |
Kwan-Hang Lam |
| author_facet |
Kwan-Hang Lam Shyh-Yu Lee 李諭 |
| author |
Shyh-Yu Lee 李諭 |
| spellingShingle |
Shyh-Yu Lee 李諭 Subharmonic Functions and The Heat Equation on Riemannian Manifolds |
| author_sort |
Shyh-Yu Lee |
| title |
Subharmonic Functions and The Heat Equation on Riemannian Manifolds |
| title_short |
Subharmonic Functions and The Heat Equation on Riemannian Manifolds |
| title_full |
Subharmonic Functions and The Heat Equation on Riemannian Manifolds |
| title_fullStr |
Subharmonic Functions and The Heat Equation on Riemannian Manifolds |
| title_full_unstemmed |
Subharmonic Functions and The Heat Equation on Riemannian Manifolds |
| title_sort |
subharmonic functions and the heat equation on riemannian manifolds |
| url |
http://ndltd.ncl.edu.tw/handle/42267739778592325918 |
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