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harmonic function; harmonic deformation; harmonic family; curve; mean value property
We study the formerly established concept of deformation of a planar curve and clarify its applicability and range. We present several applications on classical curves.
[1] Khavinson D., Lundberg E.: Linear Holomorphic Partial Differential Equations and Classical Potential Theory. Mathematical Surveys and Monographs, 232, American Mathematical Society, Providence, 2018. MR 3821527
[2] Symeonidis E.: Harmonic deformation of planar curves. Int. J. Math. Math. Sci. 2011 (2011), Art. ID 141209, 10 pages. MR 2771222
[3] Symeonidis E.: Harmonic families of planar curves. Potential Theory and Its Related Fields, RIMS Kôkyûroku Bessatsu, B43, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013, pages 171–181. MR 3220459
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