Potential Analysis

, Volume 46, Issue 1, pp 167–180 | Cite as

Darning and Gluing of Diffusions



We study darning of compact sets (darning and gluing of finite unions of compact sets), which are not thin at any of their points, in a potential-theoretic framework which may be described, analytically, in terms of harmonic kernels/harmonic functions or, probabilistically, in terms of a diffusion. This is accomplished without leaving our kind of setting so that the procedure can be iterated without any problem. It applies to darning and gluing of compacts in Euclidean spaces (manifolds) of different dimensions, which is of interest pertaining to recent studies on heat kernels.


Diffusion Brownian motion Harmonic function Harmonic kernel Darning Gluing Stable compact 

Mathematics Subject Classification (2010)

60J60 60J45 60J65 31A05 31D05 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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