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International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 141209, 10 pages
Research Article

Harmonic Deformation of Planar Curves

Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85071 Eichstätt, Germany

Received 13 November 2010; Accepted 17 January 2011

Academic Editor: Aloys Krieg

Copyright © 2011 Eleutherius Symeonidis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We establish a principle of deformation of an arbitrary planar curve, so that the integral of a harmonic function over this curve does not change. The equations of deformation can be derived from a specific “potential.” Several applications are presented.