Integral Geometric Properties of Non-compact Harmonic Spaces

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• 作者：Norbert Peyerimhoff (1)
  Evangelia Samiou (2)
  
  1. Department of Mathematical Sciences ; Durham University ; Science Laboratories South Road ; Durham ; DH1 3LE ; UK
  2. Department of Mathematics and Statistics ; University of Cyprus ; P.O. Box 20537 ; 1678 ; Nicosia ; Cyprus
  
• 关键词：Harmonic manifold ; Mean value property ; Abel transform ; Heat kernel ; 53C65 ; 43A45 ; 46F12
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：25
• 期：1
• 页码：122-148
• 全文大小：386 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

On non-compact harmonic manifolds we prove that functions satisfying the mean value property for two generic radii must be harmonic. Moreover, functions with vanishing integrals over all spheres (or balls) of two generic radii must be identically zero. We also prove results about the Cheeger constant and the heat kernel.