Harmonic mapping problem and affine capacity

Details Harmonic mapping problem and affine capacity Harmonic mapping problem and affine capacity

2010-01-13

arxiv.org/abs/1001.2124v1

Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), no. 5, 1017-1030

Mathematics

Complex Variables

14 pages, 1 figure

Scientific paper

10.1017/S0308210510000107

The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents considerable challenge and leads to several interesting open questions.

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