Abstract
We survey results and open problems in harmonic maps and minimal surface theory at a level appropriate for graduate students and others interested in contributing to the existing research. After covering some basic results, several topics are covered in more detail, including the shearing technique, inner mapping radius, convolutions, the Weierstrass Representation, determining minimal surfaces via change of variables, curvature bounds, and conjugate minimal surfaces. A variety of new and standing conjectures is included throughout. Examples are worked in detail and presented visually using ComplexTool, Mathematica, and other software packages.
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Boyd, Z., Dorff, M. (2014). Harmonic Univalent Mappings and Minimal Graphs. In: Joshi, S., Dorff, M., Lahiri, I. (eds) Current Topics in Pure and Computational Complex Analysis. Trends in Mathematics. Birkhäuser, New Delhi. https://doi.org/10.1007/978-81-322-2113-5_2
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DOI: https://doi.org/10.1007/978-81-322-2113-5_2
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